Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 78

A skateboarder of mass \(35.0 \mathrm{~kg}\) is riding her \(3.50-\mathrm{kg}\) skateboard at a speed of \(5.00 \mathrm{~m} / \mathrm{s}\). She jumps backward off her skateboard, sending the skateboard forward at a speed of \(8.50 \mathrm{~m} / \mathrm{s}\). At what speed is the skateboarder moving when her feet hit the ground?

Short Answer

Expert verified
Answer: The final velocity of the skateboarder is approximately 4.64 m/s.

Step by step solution

01

Identify the initial data

The initial data provided in the problem are the mass of the skateboarder (\(m_s = 35.0\,\text{kg}\)), the mass of the skateboard (\(m_b = 3.50\,\text{kg}\)), the initial velocity of the skateboarder and skateboard (\(v_i = 5.00\,\text{m/s}\)), and the final velocity of the skateboard (\(v_{b_f} = 8.50\,\text{m/s}\)). Our goal is to find the final velocity of the skateboarder (\(v_{s_f}\)).
02

Calculate the initial total momentum

Calculate the initial total momentum (before the skateboarder jumps off) using the equation for momentum, \(p = mv\). The total initial momentum is the combined momentum of the skateboarder and the skateboard, so \(p_{total_{initial}} = m_sv_i + m_bv_i = (35.0 + 3.50)(5.00) = 192.5\,\text{kg}\cdot\text{m/s}\).
03

Applying the conservation of momentum

According to the conservation of momentum principle, the total momentum before the jump equals the total momentum after the jump. So, \(p_{total_{initial}} = p_{total_{final}}\). Now, we need to find the final total momentum. After the jump, the momentum of the skateboard and the skateboarder is \(p_{final} = m_sv_{s_f} + m_bv_{b_f}\).
04

Calculate the final velocity of the skateboarder

Now we can set up an equation to solve for the final velocity of the skateboarder: \(192.5 = 35.0v_{s_f} + 3.50(8.50)\). Simplify the equation and solve for \(v_{s_f}\): \[192.5 = 35.0v_{s_f} + 29.75\] \[v_{s_f} = \frac{192.5-29.75}{35.0} \approx 4.64\, \text{m/s}\] The skateboarder is moving at a speed of \(4.64\,\text{m/s}\) when her feet hit the ground.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A bullet with mass \(35.5 \mathrm{~g}\) is shot horizontally from a gun. The bullet embeds in a 5.90 -kg block of wood that is suspended by strings. The combined mass swings upward, gaining a height of \(12.85 \mathrm{~cm}\). What was the speed of the bullet as it left the gun? (Air resistance can be ignored here.)

Current measurements and cosmological theories suggest that only about \(4 \%\) of the total mass of the universe is composed of ordinary matter. About \(22 \%\) of the mass is composed of dark matter, which does not emit or reflect light and can only be observed through its gravitational interaction with its surroundings (see Chapter 12). Suppose a galaxy with mass \(M_{\mathrm{G}}\) is moving in a straight line in the \(x\) -direction. After it interacts with an invisible clump of dark matter with mass \(M_{\mathrm{DM}}\), the galaxy moves with \(50 \%\) of its initial speed in a straight line in a direction that is rotated by an angle \(\theta\) from its initial velocity. Assume that initial and final velocities are given for positions where the galaxy is very far from the clump of dark matter, that the gravitational attraction can be neglected at those positions, and that the dark matter is initially at rest. Determine \(M_{\mathrm{DM}}\) in terms of \(M_{\mathrm{G}}, v_{0},\) and \(\theta\).

Attempting to score a touchdown, an 85-kg tailback jumps over his blockers, achieving a horizontal speed of \(8.9 \mathrm{~m} / \mathrm{s} .\) He is met in midair just short of the goal line by a 110 -kg linebacker traveling in the opposite direction at a speed of \(8.0 \mathrm{~m} / \mathrm{s}\). The linebacker grabs the tailback. a) What is the speed of the entangled tailback and linebacker just after the collision? b) Will the tailback score a touchdown (provided that no other player has a chance to get involved, of course)?

Cosmic rays from space that strike Earth contain some charged particles with energies billions of times higher than any that can be produced in the biggest accelerator. One model that was proposed to account for these particles is shown schematically in the figure. Two very strong sources of magnetic fields move toward each other and repeatedly reflect the charged particles trapped between them. (These magnetic field sources can be approximated as infinitely heavy walls from which charged particles get reflected elastically.) The high- energy particles that strike the Earth would have been reflected a large number of times to attain the observed energies. An analogous case with only a few reflections demonstrates this effect. Suppose a particle has an initial velocity of \(-2.21 \mathrm{~km} / \mathrm{s}\) (moving in the negative \(x\) -direction, to the left), the left wall moves with a velocity of \(1.01 \mathrm{~km} / \mathrm{s}\) to the right, and the right wall moves with a velocity of \(2.51 \mathrm{~km} / \mathrm{s}\) to the left. What is the velocity of the particle after six collisions with the left wall and five collisions with the right wall?

Two balls of equal mass collide and stick together as shown in the figure. The initial velocity of ball \(\mathrm{B}\) is twice that of ball A. a) Calculate the angle above the horizontal of the motion of mass \(\mathrm{A}+\mathrm{B}\) after the collision. b) What is the ratio of the final velocity of the mass \(A+B\) to the initial velocity of ball \(A, v_{f} / v_{A} ?\) c) What is the ratio of the final energy of the system to the initial energy of the system, \(E_{\mathrm{f}} / E_{\mathrm{i}}\) ? Is the collision elastic or inelastic?
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Scientific Method Physics

Read Explanation

Rotational Dynamics

Read Explanation

Torque and Rotational Motion

Read Explanation

Oscillations

Read Explanation

Energy Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free