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College Physics by Openstax Chapter 4 Problem 7

(a) If the rocket sled shown in Figure 4.31 starts with only one rocket burning, what is the magnitude of its acceleration? Assume that the mass of the system is 2100 kg, the thrust $T$ is $2.4 \times 10^{4}$ N, and the force of friction opposing the motion is known to be 650 N. (b) Why is the acceleration not one-fourth of what it is with all rockets burning?

Solution:

Considering the direction of motion as the positive direction, we are given the following: $T=2.4 \times 10^4 \ \text{N}$ , $f=-650 \ \text{N}$ , and mass, $m=2100 \ \text{kg}$ .

Part A. The magnitude of the acceleration can be computed using Newton’s Second Law of Motion.

\begin{align*} \Sigma F & =ma \\ 2.4\times 10^4 \ \text{N}-650 \ \text{N} & = 2100 \ \text{kg}\times a \\ 23350 & = 2100 a \\ \frac{23350}{2100} & = \frac{\cancel{2100} a}{\cancel{2100}} \\ a & = \frac{23350}{2100} \\ a & = 11 \ \text{m/s}^2 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

Part B. The acceleration is not one-fourth of what it was with all rockets burning because the frictional force is still as large as it was with all rockets burning. $\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)$

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College Physics by Openstax Chapter 4 Problem 6

The same rocket sled drawn in Figure 4.30 is decelerated at a rate of 196 m/s². What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2100 kg.

Solution:

Since the rockets are off, the only force acting on the sled is the friction $f$ . This force is against the direction of motion. By using Newton’s Second Law of Motion, we have.

\begin{align*} \Sigma F & = ma \\ -f & = ma \\ -f & = \left( 2100 \ \text{kg} \right)\left( -196 \ \text{m/s}^{2} \right) \\ -f & = -411600 \ \text{N} \\ f & = 411600 \ \text{N} \\ f & = 411.6 \ \text{kN} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

The force necessary to produce the given deceleration is 411.6 kN.

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College Physics by Openstax Chapter 4 Problem 5

In Figure 4.7, the net external force on the 24-kg mower is stated to be 51 N. If the force of friction opposing the motion is 24 N, what force F (in newtons) is the person exerting on the mower? Suppose the mower is moving at 1.5 m/s when the force F is removed. How far will the mower go before stopping?

Solution:

We can isolate the mower and expose the forces acting on it. This is the free-body diagram.

The free-body diagram of the mower: the force F exerted by the person and the friction force f exerted by the ground on the mower.

There are two forces acting on the mower in the horizontal directions:

$\textbf{F}:$ This is the force exerted by the person on the mower, and it is going to the right. This is the first unknown in the problem. We treat this as a positive force since it is directed to the right. The value of this force is $F=51 \ \text{N}$
$\textbf{f}:$ This is the friction force directed opposite the motion of the mower. We treat this as a negative force because it is directed to the left. The value of this force is $f=24 \ \text{N}$ .

Part A. The third force in the figure is the net force, $F_{net}$ . This is the vector sum of the forces $F$ and $f$ . That is

\begin{align*} F_{net} & =F-f \\ 51 \ \text{N} & = F-24 \ \text{N} \\ F & = 51 \ \text{N} +24 \ \text{N} \\ F & = 75 \ \text{N} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

The person should exert a force of 75 N to produce a net force of 51 N.

Part B. When the force F is removed, the friction is now the only force acting on the mower. The friction is acting opposite the direction of motion. The direction of motion is indicated by the blue arrow in the figure below, and the friction force is the red arrow.

The free-body diagram of the mower when force F is removed.

Using Newton’s Second Law, we can solve for the deceleration of the mower.

\begin{align*} \Sigma F & = ma \\ -24 \ \text{N} & = \left( 24 \ \text{kg} \right) \ a \\ \frac{-24 \ \text{N}}{24 \ \text{kg}} & = \frac{\cancel{24 \ \text{kg}}\ \ a}{\cancel{24 \ \text{kg}}} \\ a & = \frac{-24 \ \text{N}}{24 \ \text{kg}} \\ a & = -1 \ \text{m/s}^{2} \\ \end{align*}

Using this deceleration computed above, we can solve for the distance traveled by the mower before coming to stop.

\begin{align*} \left( v_{f} \right)^{2} & = \left( v_{o} \right)^{2}+2a\Delta x \\ \left( 0 \ \text{m/s} \right)^{2} & = \left( 1.5 \ \text{m/s} \right)^{2}+2\left( -1 \ \text{m/s}^{2} \right)\Delta x \\ 0 & = 2.25-2 \Delta x \\ 2 \Delta x & = 2.25 \\ \frac{\cancel{2}\Delta x}{\cancel{2}} & =\frac{2.25}{2} \\ \Delta x & = 1.125 \ \text{m} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

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College Physics by Openstax Chapter 4 Problem 4

Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be 0.893 m/s². (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which recoil of the vehicle is avoided.

Solution:

We are given the following: $\sum F = 50.0 \ \text{N}$ , and $a=0.893 \ \text{m/s}^{2}$ .

Part A. We can solve for the mass, $m$ by using Newton’s second law of motion.

\begin{align*} \sum F & = ma \\ 50.0 \ \text{N} & = m \left( 0.893 \ \text{m/s}^{2} \right) \\ m & = \frac{50.0 \ \text{N}}{0.893 \ \text{m/s}^{2}} \\ m & = 56.0 \ \text{kg}\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

Part B. The measured acceleration is equal to the sum of the accelerations of the astronauts and the ship. That is

a_{measured}=a_{astronaut}+a_{ship}

If a force acting on the astronaut came from something other than the spaceship, the spaceship would not undergo a recoil. $\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)$

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College Physics by Openstax Chapter 4 Problem 3

A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate its acceleration.

Solution:

From Newton’s Second Law of Motion, $\sum F =ma$ . Substituting the given values, we have

\begin{align*} \sum F & = ma \\ 60.0 \ \text{N} & = \left( 4.50 \ \text{kg} \right) \ a \\ a & = \frac{60.0 \ \text{N}}{4.50 \ \text{kg}} \\ a & = 13.3 \ \text{m/s}^{2} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

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College Physics by Openstax Chapter 2 Problem 57

A coin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. For the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.

Solution:

Part A

Consider Figure A.

We are interested in two positions. Position 1 is where the coin is dropped. At this position, the coin is 300 m above the ground, the time is 0 s, and the velocity is 10.0 m/s upward.

Position 2 is the highest point of the coin reaches. At this position, the velocity is equal to 0 m/s.

Position 1 is the initial position and position 2 is the final position. Solve for the value of y₂.

\begin{align*} \left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 +2a \Delta y \\ \Delta y & = \frac{\left( v_{y_2} \right)^2 - \left( v_{y_1} \right)^2}{2a} \\ y_2 - y_1 & = \frac{\left( v_{y_2} \right)^2 - \left( v_{y_1} \right)^2}{2a} \\ y_2& = \frac{\left( v_{y_2} \right)^2 - \left( v_{y_1} \right)^2}{2a} +y_1 \\ y_2 & = \frac{\left( 0 \ \text{m/s} \right)^2-\left( 10.0\ \text{m/s} \right)^2}{2\left( -9.81 \ \text{m/s}^2 \right)}+300\ \text{m} \\ y_2 & =305 \ \text{m} \ \qquad {\color{DarkOrange} \left( \text{Answer} \right)}\\ \end{align*}

$\therefore$ The maximum height reached by the coin is about 305 meters from the ground.

Part B

We do not know the position 4 seconds after the coin has been released, the answer can be above or below the initial point. We can actually use one of the kinematical equations to solve for the final position given the time. Here, the initial position is the point of release and the final position is the point of interest at 4.00 seconds after release.

\begin{align*} \Delta y & = v_{y_1}t+\frac{1}{2}at^2 \\ y_2 - y_1 & = v_{y_1}t+\frac{1}{2}at^2 \\ y_2 & = y_1 + v_{y_1}t+\frac{1}{2}at^2 \\ y_2 & = 300\ \text{m} +\left( 10\ \text{m/s} \right)\left( 4.00\ \text{s} \right)+\frac{1}{2}\left( -9.81\ \text{m/s}^2 \right)\left( 4.00\ \text{s} \right)^2\\ y_2 & = 261.52\ \text{m} \\ y_2 & = 262\ \text{m}\ \qquad \ {\color{DarkOrange} \left( \text{Answer} \right)} \\ \end{align*}

$\therefore$ The coin is at a height of 262 meters above the ground 4.00 seconds after release. That is, the coin is already dropping and it is already below the release point.

Solving for the velocity 4.00 seconds after release considering the same initial and final position.

\begin{align*} v_{y_2} & = v_{y_1}+at \\ v_{y_2} & = 10\ \text{m/s} + \left( -9.81\ \text{m/s}^2 \right)\left( 4.00 \ \text{s} \right) \\ v_{y_2} & = -29.2\ \text{m/s} \ \qquad \ {\color{DarkOrange} \left( \text{Answer} \right)} \end{align*}

$\therefore$ The coin has a velocity of 29.2 m/s directed downward 4.00 seconds after it is released. This confirms that the coin is indeed moving downwards at this point.

Part C

Considering figure C, we have two positions. Position 1 is the point of release 300 m above the ground with a velocity of 10 m/s upward. This is time 0 s.

The second position is at the ground where y=0 m. We are interested at the time in this position.

Considering position 1 as the initial position and position 2 as the final position.

\begin{align*} \Delta y & = v_{y_1} \Delta t+\frac{1}{2}a\left( \Delta t \right)^2 \\ y_2-y_1 & = v_{y_1}t+\frac{1}{2}at^2 \\ 0\ \text{m}-300\ \text{m} & = \left( 10 \ \text{m/s} \right)t+\frac{1}{2}\left( -9.81\ \text{m/s}^2 \right)t^2 \\ -300 & = 10t-4.905t^2 \\ 4.905t^2-10t-300 & = 0 \\ \end{align*}

Solve for the value of t using the quadratic formula with a=4.905, b=-10, and c=-300.

\begin{align*} t & = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\\ t & = \frac{-\left( -10 \right) \pm \sqrt{\left( 10 \right)^2-4\left( 4.905 \right)\left( -300 \right)}}{2\left( 4.905 \right)}\\ t & = 8.91 \ \text{s} \ \qquad \ {\color{DarkOrange} \left( \text{Answer} \right)} \end{align*}

$\therefore$ The time is about 8.91 seconds before the coin hits the ground.

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College Physics by Openstax Chapter 2 Problem 56

A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts 0.0800 ms (8.00×10⁻⁵ s) . (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?

Solution:

Part A

For this part, we shall consider Figure A.

We will be considering the two positions as shown. The first position is when the ball is dropped from a height of 1.50 meters. For this position, we know that y₁=1.50 m, t₁=0 s, and v_y1=0 m/s.

Position 2 is immediately after the ball hits the floor. For this position, we do not the time elapse and the velocity but we know that the height is zero. That is y₂=0 m.

Position 1 is the initial position and position 2 is the final position. Solving for v_y2, we have

\begin{align*} \left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \Delta y \\ \left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \left( y_2 - y_1 \right) \\ v_{y_2} & = \sqrt{\left( v_{y_1} \right)^2 + 2 a \left( y_2 - y_1 \right)} \\ v_{y_2} & = - \sqrt{\left( 0 \right)^2+2\left( -9.81\ \text{m/s}^2 \right)\left( 0\ \text{m} - 1.50\ \text{m} \right)} \\ v_{y_2} & = - 5.42 \ \text{m/s} \qquad {\color{DarkOrange} \left( \text{Answer} \right)} \end{align*}

$\therefore$ The steel ball has a velocity of about 5.42 m/s directed downward when it strikes the floor.

Part B

Figure B shows the two positions we are interested in to solve for this part.

Position 1 is at the floor immediately just after the ball hits it. At this initial position, we have y1=0 m, and t1= 0 s. We do not know the velocity at this point.

At position 2, the ball bounced back to its second peak. We know that at the peak of a free falling body, the velocity is zero. So, for this final position, we have y₂=1.45 m, and v_y2=0 m/s. We do not know the time at this position.

Position 1 is the initial position while position 2 is the final position. Solving for the initial velocity we have

\begin{align*} \left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \Delta y \\ \left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \left( y_2 - y_1 \right) \\ \left( v_{y_1} \right)^2 & = \left( v_{y_2} \right)^2 - 2 a \left( y_2 - y_1 \right) \\ v_{y_1} & = \sqrt{\left( v_{y_2} \right)^2 - 2 a \left( y_2 - y_1 \right)} \\ v_{y_1} & = \sqrt{\left( 0 \ \text{m/s} \right)^2 -2\left( -9.81 \ \text{m/s}^2 \right) \left( 1.45 \ \text{m} - 0 \ \text{m} \right) }\\ v_{y_1} & = 5.33 \ \text{m/s} \qquad {\color{DarkOrange} \left( \text{Answer} \right)} \end{align*}

$\therefore$ The steel ball has a velocity of about 5.33 m/s directed upward immediately after it leaves the floor.

Part C

From our answers in Part A and Part B, we have a change in velocity from -5.42 m/s to 5.33 m/s. So, in this case the initial velocity is v₁=-5.42 m/s and the final velocity is v₂=5.33 m/s. We can compute for the acceleration:

\begin{align*} a & = \frac{\Delta v}{\Delta t} \\ a & = \frac{v_2-v_1}{\Delta t} \\ a & = \frac{5.33 \ \text{m/s} - \left( -5.42 \ \text{m/s} \right)}{8.00 \times 10^{-5} \ \text{s}} \\ a & = 134,375 \ \text{m/s}^2 \\ a & = 1.34 \times 10^{5} \text{m/s}^2 \ \qquad {\color{DarkOrange} \left( \text{Answer} \right)}\\ \end{align*}

Part D

The period of compression happens when the ball has a velocity of -5.42 m/s until it reaches 0 m/s. We shall solve for the change in displacement for this two given velocities. The initial velocity is -5.42 m/s and the final velocity is 0 m/s. The acceleration during this period is the one solved in Part C, a=1.34×10⁵ m/s².

\begin{align*} \left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \Delta y \\ \Delta y & = \frac{\left( v_{y_2} \right)^2 - \left( v_{y_1} \right)^2}{2 a} \\ \Delta y & = \frac{\left( 0 \ \text{m/s} \right)^2 - \left( -5.42 \ \text{m/s} \right)^2}{2\left( 1.34 \times 10^5 \ \text{m/s}^2 \right)}\\ \Delta y & = -0.000110 \ \text{m} \\ \Delta y & = -1.10 \times 10^{-4} \ \text{m} \ \qquad \ {\color{DarkOrange} \left( \text{Answer} \right)}\\ \end{align*}

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College Physics by Openstax Chapter 2 Problem 54

A ball is thrown straight up. It passes a 2.00-m-high window 7.50 m off the ground on its path up and takes 0.312 s to go past the window. What was the ball’s initial velocity? Hint: First consider only the distance along the window, and solve for the ball’s velocity at the bottom of the window. Next, consider only the distance from the ground to the bottom of the window, and solve for the initial velocity using the velocity at the bottom of the window as the final velocity.

Solution:

First, we have the position 1 where the motion starts. Here, we know that y<sub>1</sub>=0, t<sub>1</sub>=0, and v<sub>y1</sub>=0.

Position 2 is at the bottom of the window. We know that it is 7.50 meters from where the motion started. So we have y<sub>2</sub>=7.50 meters. We do not know the time and velocity at this point.

Then we have position 3 at the top of the window where the overall height is 9.50 meters, y<sub>3</sub>=9.50. We also do not know the velocity and time elapsed in this position. — *Figure A*

Consider Figure A. We shall be considering the three positions shown.

First, we have position 1 where the motion starts. Here, we know that y₁=0 and t₁=0, but we do not know v_y1.

Position 2 is at the bottom of the window. We know that it is 7.50 meters from where the motion started. So we have y₂=7.50 meters. We do not know the time and velocity at this point.

Then we have position 3 at the top of the window where the overall height is 9.50 meters, y₃=9.50. We also do not know the velocity and time elapsed in this position.

Consider positions 2 and 3. The initial position in this case is at position 2 and the final position is at position 3. We know that the difference of time between this two positions is 0.312 seconds. We can say that

t_3 =t_2+0.312 \ \text{s} \\ t_3-t_2 = 0.312\ \text{s}

Using the same 2 positions still, we have

\begin{align*} y_3 & = y_2 + v_{y_2} \Delta t+\frac{1}{2}a\left( \Delta t \right)^2 \\ 9.50\ \text{m} & = 7.50\ \text{m} + v_{y_2} \left( t_3-t_2 \right)+\frac{1}{2}a\left( t_3-t_2 \right)^2 \\ 9.50\ \text{m}-7.50\ \text{m} & = v_{y_2}\left( 0.312\ \text{s} \right)+\frac{1}{2}\left( -9.81\ \text{m/s}^2 \right)\left( 0.312\ \text{s} \right)^2\\ 2.00\ \text{m} & = 0.312\ \text{s} \left( v_{y_2} \right)-0.4775\ \text{m} \\ 0.312\ \text{s} \left( v_{y_2} \right) & = 2.00\ \text{m}+0.4775\ \text{m} \\ 0.312\ \text{s} \left( v_{y_2} \right) & = 2.4775\ \text{m} \\ v_{y_2}& =\frac{2.4775\ \text{m}}{0.312\ \text{s}} \\ v_{y_2}& = 7.94\ \text{m/s} \end{align*}

We have computed the velocity of the ball at the bottom of the window.

Next, we shall consider positions 1 and 2. In this consideration, position 1 will be considered the initial position while position2 is the final position.

\begin{align*} \left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 +2a \Delta y \\ \left( 7.94\ \text{m/s} \right)^2 & = \left( v_{y_1} \right)^2 + 2\left( -9.81 \ \text{m/s}^2 \right)\left( 7.50\ \text{m}-0 \right)\\ \left( v_{y_1} \right)^2 & = \left( 7.94\ \text{m/s} \right)^2- 2\left( -9.81 \ \text{m/s}^2 \right)\left( 7.50\ \text{m}-0 \right)\\ v_{y_1} & = + \sqrt{ \left( 7.94\ \text{m/s} \right)^2- 2\left( -9.81 \ \text{m/s}^2 \right)\left( 7.50\ \text{m}-0 \right)} \\ v_{y_1} & = + 14.5\ \text{m/s}\qquad {\color{DarkOrange} \left( \text{Answer} \right) } \end{align*}

$\therefore$ The ball’s initial velocity is about 14.5 m/s upward.

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College Physics by Openstax Chapter 3 Problem 36

The world long jump record is 8.95 m (Mike Powell, USA, 1991). Treated as a projectile, what is the maximum range obtainable by a person if he has a take-off speed of 9.5 m/s? State your assumptions.

Solution:

We are required to solve for the maximum distance. To do this, we can use the formula for the range of a projectile motion. However, we need the following assumptions:

The jumper leaves the ground in a 45° angle from the horizontal, for maximum horizontal displacement.
The jumper is on level ground, and the motion started from the ground.

The formula for range is

\text{R}=\frac{\text{v}_{\text{o}}^2\sin 2\theta _{\text{o}}}{\text{g}}

Since we are already given the necessary details, we can now solve for the range.

\begin{align*} \text{R}&=\frac{\left(9.5\:\text{m/s}\right)^2\:\sin 90^{\circ} }{9.81\:\text{m/s}^2}\\ \text{R}&=9.20\:\text{m}\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)\\ \end{align*}

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College Physics by Openstax Chapter 3 Problem 33

The cannon on a battleship can fire a shell a maximum distance of 32.0 km. (a) Calculate the initial velocity of the shell. (b) What maximum height does it reach? (At its highest, the shell is above 60% of the atmosphere—but air resistance is not really negligible as assumed to make this problem easier.) (c) The ocean is not flat, because the Earth is curved. Assume that the radius of the Earth is 6.37×10³ km . How many meters lower will its surface be 32.0 km from the ship along a horizontal line parallel to the surface at the ship? Does your answer imply that error introduced by the assumption of a flat Earth in projectile motion is significant here?

Solution:

Part A

We are given the range of the projectile motion. The range is 32.0 km. We also know that for the projectile to reach its maximum distance, it should be fired at 45°. So from the formula of range,

\displaystyle \text{R}=\frac{\text{v}_0^2\:\sin 2\theta _0}{\text{g}}

we can say that $\sin 2\theta _0=\sin \left(2\times 45^{\circ} \right)=\sin 90^{\circ} =1$ . So, we have

\displaystyle \text{R}=\frac{\text{v}_0^2}{\text{g}}

We can solve for v₀ in terms of the other variables. That is

\displaystyle \text{v}_0=\sqrt{\text{gR}}

Substituting the given values, we have

\begin{align*} \displaystyle \text{v}_0 & =\sqrt{\left(9.81\:\text{m/s}^2\right)\left(32\times 10^3\:\text{m}\right)} \\ \displaystyle \text{v}_0 & =560.29\:\text{m/s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)\\ \end{align*}

Part B

We are solving for the maximum height here, which happened at the mid-flight of the projectile. The vertical velocity at this point is zero. Considering all this, the formula for the maximum height is derived to be

\displaystyle \text{h}_{\text{max}}=\frac{\text{v}_{0_y}^2}{2\text{g}}

The initial vertical velocity, v_0y, is calculated as

\begin{align*} \text{v}_{\text{0y}} & =\text{v}_0\sin \theta _0 \\ & =\left(560.29\:\text{m/s}\right)\sin 45^{\circ} \\ & =396.18\:\text{m/s} \end{align*}

Therefore, the maximum height is

\begin{align*} \text{h}_{\text{max}} & =\frac{\left(396.18\:\text{m/s}\right)^2}{2\left(9.81\:\text{m/s}^2\right)} \\ \text{h}_{\text{max}} & =8000\:\text{m} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \\ \end{align*}

Part C

Consider the following figure

A right triangle is formed with the legs, the horizontal distance and the radius of the earth, and the hypotenuse is the sum of the radius of the earth and the distance d, which is the unknown in this problem. Using Pythagorean Theorem, and converting all units to meters, we have

\begin{align*} \text{R}^2+\left(32.0\times 10^3\:\text{m}\right)^2 & =\left(\text{R}+\text{d}\right)^2 \\ \left(6.37\times 10^6\:\text{m}\right)^2+\left(32.0\times 10^3\:\text{m}\right)^2 & =\left(6.37\times 10^6+\text{d}\right)^2 \\ \text{d} & =\sqrt{\left(6.37\times \:10^6\:\right)^2+\left(32.0\times 10^3\:\right)^2}-6.37\times \:10^6 \\ \text{d} & =80.37\:\text{m} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \\ \end{align*}

This error is not significant because it is only about 1% of the maximum height computed in Part B.

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College Physics by Openstax Chapter 4 Problem 7

College Physics by Openstax Chapter 4 Problem 6

The same rocket sled drawn in Figure 4.30 is decelerated at a rate of 196 m/s². What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2100 kg.

College Physics by Openstax Chapter 4 Problem 5

College Physics by Openstax Chapter 4 Problem 4

College Physics by Openstax Chapter 4 Problem 3

A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate its acceleration.

College Physics by Openstax Chapter 2 Problem 57

A coin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. For the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.

College Physics by Openstax Chapter 2 Problem 56

College Physics by Openstax Chapter 2 Problem 54

College Physics by Openstax Chapter 3 Problem 36

The world long jump record is 8.95 m (Mike Powell, USA, 1991). Treated as a projectile, what is the maximum range obtainable by a person if he has a take-off speed of 9.5 m/s? State your assumptions.

College Physics by Openstax Chapter 3 Problem 33

The same rocket sled drawn in Figure 4.30 is decelerated at a rate of 196 m/s2. What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2100 kg.

A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate its acceleration.

A coin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. For the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.

The world long jump record is 8.95 m (Mike Powell, USA, 1991). Treated as a projectile, what is the maximum range obtainable by a person if he has a take-off speed of 9.5 m/s? State your assumptions.

The same rocket sled drawn in Figure 4.30 is decelerated at a rate of 196 m/s². What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2100 kg.