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Chapter 4: Problem 1

As you walk briskly down the street, you toss a small ball into the air. (a) If you want the ball to land in your hand when it comes back down, should you toss the ball straight upward, in a forward direction, or in a backward direction, relative to your body? (b) Choose the best explanation from among the following: I. If the ball is thrown straight up you will leave it behind. II. You have to throw the ball in the direction you are walking. III. The ball moves in the forward direction with your walking speed at all times.

Short Answer

Expert verified
Toss the ball straight upward. Explanation III is correct.

Step by step solution

01

Analyze the Ball's Motion

Let's consider the motion of the ball relative to your motion. When you toss the ball, it already has the forward velocity that you have from walking.
02

Determine the Optimal Toss Direction

To catch the ball, you need it to follow a path that will allow it to return to your hand. Since the ball already has a forward velocity, throwing it straight up ensures it maintains that forward velocity and falls back along your path.
03

Evaluate the Given Explanations

Review the explanations: - I. Incorrect, as the ball moves forward along with you at your walking speed; it won't be left behind if tossed straight up. - II. Partially correct but not necessary as explained. - III. Correct, because it states the ball will continue moving forward with your initial walking speed.
04

Conclusion on the Toss Direction

You should toss the ball straight upward. This ensures that the ball's forward velocity remains the same, allowing it to be caught when it returns to its original vertical position.
05

Choose the Best Explanation

Explanation III is the most appropriate choice as it correctly describes how the ball maintains your forward walking speed at all times.

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Key Concepts

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

Relative Motion
Understanding the concept of relative motion is crucial when considering how objects move in relation to each other. In the exercise, as you walk down the street and toss the ball, both you and the ball are involved in relative motion. Here鈥檚 what this means:
  • The ball already shares your forward velocity as it was initially at rest in your hand while you were moving.
  • When you toss the ball straight up, it continues to carry the same forward velocity as your motion.
This is why throwing it straight upward doesn鈥檛 cause the ball to fall behind you. Relative motion showcases that while you keep walking, the ball keeps up with you because it had a shared velocity to start with. So, you will still be beneath it when it comes down.
Velocity
In physics, velocity is a vector quantity that describes both the speed and direction of an object's motion.
  • Your walking provides a constant forward velocity to both you and the ball when thrown.
  • When the ball is tossed straight upward, its vertical velocity changes due to gravity, but its horizontal component remains unchanged at your walking speed.
This means the horizontal motion of the ball isn't affected by the vertical toss. Despite the ball moving up and down, it also moves forward at your initial speed, ensuring it lands back in your hand. This concept ties directly to explanation III from the exercise solution.
Kinematics
Kinematics involves studying the motion of objects without considering the forces causing it. When you throw the ball in the air, kinematic equations can describe its flight path:
  • The vertical motion is influenced by gravity, which decelerates the ball as it goes up and accelerates it as it comes back down.
  • The horizontal motion remains constant and mirrors your walking speed.
Analyzing both the vertical and horizontal movements separately allows you to predict the path the ball will take. Since the horizontal motion isn鈥檛 affected by gravity, it ensures the ball follows you as you walk. Thus, using kinematic principles, this exercise illustrates how both vertical and horizontal motions combine to predict the ball鈥檚 trajectory back into your hand.

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Most popular questions from this chapter

Suppose the ball is dropped at the horizontal distance of \(5.50 \mathrm{m},\) but from a new height of \(5.00 \mathrm{m} .\) The dolphin jumps with the same speed of \(12.0 \mathrm{m} / \mathrm{s}\). (a) What launch angle must the dolphin have if it is to catch the ball? (b) At what height does the dolphin catch the ball in this case? (c) What is the minimum initial speed the dolphin must have to catch the ball before it hits the water?

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