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Chapter 27: Problem 3

A boy on a skateboard coasts along at 5 m/s. He has a ball that he can throw at a speed of 10 m/s. What is the ball鈥檚 speed relative to the ground if he throws the ball (a) forward or (b) backward?

Short Answer

Expert verified
The speed of the ball relative to the ground is 15 m/s when thrown forward and 5 m/s when thrown backward.

Step by step solution

01

Determine the Direction of Motion

Identify the direction of skateboard's motion as positive direction. The board is moving forward with a speed of 5 m/s.
02

Calculate the Ball鈥檚 Speed When Thrown Forward

When the ball is thrown forward (in the same direction as the skateboard's motion), the speeds add up. Hence, the speed of the ball relative to the ground is the sum of the speed of the skateboard and the speed at which the boy throws the ball, i.e., \(5 m/s + 10 m/s = 15 m/s\).
03

Compute the Ball鈥檚 Speed When Thrown Backward

When the ball is thrown backward (in the opposite direction to the skateboard's motion), the speeds subtract. Thus, the speed of the ball relative to the ground is the difference between the speed of the skateboard and the speed at which the boy throws the ball, i.e., \(10 m/s - 5 m/s = 5 m/s\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kinematics
Kinematics is the branch of physics that deals with the motion of objects without considering the forces causing the motion. It helps us understand how different objects move in space and time. In kinematics, we focus on key aspects of motion like speed, velocity, and acceleration.

To break it down simply:
  • Speed is the distance an object travels per unit of time. It's a scalar quantity, which means it only considers magnitude.
  • Velocity, on the other hand, is speed in a particular direction. This makes it a vector quantity with both magnitude and direction.
  • Acceleration refers to the rate at which an object changes its velocity.
In our skateboard scenario, kinematics helps us analyze how the skateboard and ball move in relation to each other and to the ground. Understanding these motions is key to solving the problem.
Motion
The concept of motion refers to the change in the position of an object over time. It's fundamental to physics and particularly kinematics. Grasping how things move involves understanding various types of motion such as linear, circular, and projectile.

In the skateboard example, we're dealing with linear motion, where both the skateboard and the ball move along a straight path. Let's clarify this further:
  • Linear Motion: This is motion along a straight line, which in this situation, includes the skateboard moving forward or backward, and the ball following similar paths.
  • By calculating the ball's speed when thrown forward or backward, we observe changes in this linear motion.
Understanding motion provides the basis for comprehending how different velocities affect the speed of the ball relative to the ground.
Frame of Reference
A frame of reference is a viewpoint from which motion is observed and measured. It's like choosing a camera angle to view the scene of a movement. By defining a frame of reference, we can make sense of how fast or in which direction objects are moving.

In physics, there are often multiple valid frames of reference:
  • The ground is a common frame of reference in everyday situations. It's used to measure the absolute motion of objects. In our exercise, the speed of the skateboard and the ball are measured with respect to the ground.
  • The skateboard itself can also act as a moving frame of reference. From this viewpoint, if the boy throws the ball, the relative speed would be purely the speed at which he throws it, either forward or backward.
Choosing the right frame of reference simplifies problems and helps us understand relative velocities by interpreting how an object appears to move against the chosen background or point of view.

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Most popular questions from this chapter

A rocket traveling at 0.500c sets out for the nearest star, Alpha Centauri, which is 4.25 ly away from earth. It will return to earth immediately after reaching Alpha Centauri. What distance will the rocket travel and how long will the journey last according to (a) stay-at-home earthlings and (b) the rocket crew?

An astronaut in a spacesuit on a spacewalk is a completely sealed system, with no matter lost or gained. In principle, the energy the astronaut uses will result in a decrease in mass. Suppose on a gentle spacewalk his metabolic power plus the power of the suit is 250 W. What is the change in mass, in kg, on a 1 hour spacewalk

A rocket cruising past earth at 0.800c shoots a bullet out the back door, opposite the rocket鈥檚 motion, at 0.900c relative to the rocket. What is the bullet鈥檚 speed relative to the earth?

The sun radiates energy at the rate \(3.8 \times 10^{26}\) W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is \(2.0 \times 10^{30} \mathrm{kg}\) a. How much mass does the sun lose each year? b. What percentage is this of the sun"s total mass? c. Estimate the lifetime of the sun.

Your 1000-m-long starship has warning lights at each end that, to you, flash simultaneously every minute. You are moving directly away from the planet Zerkon at 0.70c. To a Zerkonian, do the lights flash simultaneously? If not, which flashes first the light at the front of your ship or the trailing one?
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