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Chapter 7: Problem 75

A 60.0 -kg astronaut inside a 7.00 -m-long space capsule of mass \(500 . \mathrm{kg}\) is floating weightlessly on one end of the capsule. He kicks off the wall at a velocity of \(3.50 \mathrm{~m} / \mathrm{s}\) toward the other end of the capsule. How long does it take the astronaut to reach the far wall?

Short Answer

Expert verified
Answer: It takes approximately 1.79 seconds for the astronaut to reach the far wall of the space capsule.

Step by step solution

01

Calculate the initial and final momentum of the astronaut and the capsule

Before the astronaut kicks off, both the astronaut and the capsule are at rest, so their initial momenta are zero. When the astronaut kicks off with a velocity of \(3.50\,\text{m/s}\), the final momentum of the astronaut (\(P_{\text{astronaut}}\)) is given by: \(P_{\text{astronaut}}= m_{\text{astronaut}} \cdot v_{\text{astronaut}} = 60.0\,\text{kg}\cdot 3.50\,\text{m/s}= 210\,\text{kg·m/s}\) According to the conservation of momentum principle, the final momentum of the capsule (\(P_{\text{capsule}}\)) should be equal and opposite to that of the astronaut. \(P_{\text{capsule}} = -P_{\text{astronaut}} = -210\,\text{kg·m/s}\)
02

Calculate the final velocity of the capsule

To find the final velocity of the capsule (\(v_{\text{capsule}}\)), we can use the following equation: \(v_{\text{capsule}} = \dfrac{P_{\text{capsule}}}{m_{\text{capsule}}} = \dfrac{-210\,\text{kg·m/s}}{500\,\text{kg}} = -0.42\,\text{m/s}\)
03

Calculate the relative velocity between the astronaut and the capsule

The relative velocity between the astronaut and the capsule (\(v_{\text{relative}}\)) is given by: \(v_{\text{relative}} = v_{\text{astronaut}} - v_{\text{capsule}} = 3.50\,\text{m/s} - (-0.42\,\text{m/s}) = 3.92\,\text{m/s}\)
04

Calculate the time taken by the astronaut to reach the far wall

The distance between the astronaut and the far wall of the capsule is 7.00 m: distance = 7.00 m To find the time taken by the astronaut to reach the far wall, we can use the following equation: time = \(\dfrac{\text{distance}}{v_{\text{relative}}} = \dfrac{7.00\,\text{m}}{3.92\,\text{m/s}} = 1.79\,\text{s}\) Therefore, it takes approximately 1.79 seconds for the astronaut to reach the far wall of the space capsule.

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Most popular questions from this chapter

Here is a popular lecture demonstration that you can perform at home. Place a golf ball on top of a basketball, and drop the pair from rest so they fall to the ground. (For reasons that should become clear once you solve this problem, do not attempt to do this experiment inside, but outdoors instead!) With a little practice, you can achieve the situation pictured here: The golf ball stays on top of the basketball until the basketball hits the floor. The mass of the golf ball is \(0.0459 \mathrm{~kg}\), and the mass of the basketball is \(0.619 \mathrm{~kg}\). you can achieve the situation pictured here: The golf ball stays on top of the basketball until the basketball hits the floor. The mass of the golf ball is \(0.0459 \mathrm{~kg}\), and the mass of the basketball is \(0.619 \mathrm{~kg}\). a) If the balls are released from a height where the bottom of the basketball is at \(0.701 \mathrm{~m}\) above the ground, what is the absolute value of the basketball's momentum just before it hits the ground? b) What is the absolute value of the momentum of the golf ball at this instant? c) Treat the collision of the basketball with the floor and the collision of the golf ball with the basketball as totally elastic collisions in one dimension. What is the absolute magnitude of the momentum of the golf ball after these collisions? d) Now comes the interesting question: How high, measured from the ground, will the golf ball bounce up after its collision with the basketball?

One of the events in the Scottish Highland Games is the sheaf toss, in which a \(9.09-\mathrm{kg}\) bag of hay is tossed straight up into the air using a pitchfork. During one throw, the sheaf is launched straight up with an initial speed of \(2.7 \mathrm{~m} / \mathrm{s}\). a) What is the impulse exerted on the sheaf by gravity during the upward motion of the sheaf (from launch to maximum height)? b) Neglecting air resistance, what is the impulse exerted by gravity on the sheaf during its downward motion (from maximum height until it hits the ground)? c) Using the total impulse produced by gravity, determine how long the sheaf is airborne.

7.57 A 1439 -kg railroad car traveling at a speed of \(12 \mathrm{~m} / \mathrm{s}\) strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed (in \(\mathrm{m} / \mathrm{s})\) afterward?

In many old Western movies, a bandit is knocked back \(3 \mathrm{~m}\) after being shot by a sheriff. Which statement best describes what happened to the sheriff after he fired his gun? a) He remained in the same position. b) He was knocked back a step or two. c) He was knocked back approximately \(3 \mathrm{~m}\). d) He was knocked forward slightly. e) He was pushed upward.

When hit in the face, a boxer will "ride the punch"; that is, if he anticipates the punch, he will allow his neck muscles to go slack. His head then moves back easily from the blow. From a momentum-impulse standpoint, explain why this is much better than stiffening his neck muscles and bracing himself against the punch.
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