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Chapter 2: Problem 12

You toss a small ball vertically up in the air. How are the velocity and acceleration vectors of the ball oriented with respect to one another during the ball's flight up and down?

Short Answer

Expert verified
Answer: During the upward flight, the velocity vector points upward and the acceleration vector (due to gravity) points downward. At the highest point, the velocity vector is momentarily zero (no direction) while the acceleration vector points downward. During the downward flight, both the velocity and acceleration vectors point downward.

Step by step solution

01

Identify the given information

The exercise tells us that a ball is tossed vertically up in the air. The only acceleration acting on the ball is due to gravity. The acceleration due to gravity has a constant value, and it points downwards.
02

Analyze the upward flight of the ball

During the upward flight, the velocity vector of the ball is pointing upward since the ball is moving up. However, the acceleration due to gravity is still acting downward. So during this phase, the two vectors have opposite directions.
03

Analyze the highest point of the flight

At the highest point of the ball's flight, the velocity vector becomes momentarily zero since the ball is neither moving up nor down. The acceleration due to gravity remains constant and points downward. At this point, the velocity vector can be regarded as having no direction, while the acceleration vector has a downward orientation.
04

Analyze the downward flight of the ball

During the downward flight, the velocity vector of the ball is pointing downward since the ball is moving in that direction. At the same time, the acceleration due to gravity continues to act downward. In this phase, the two vectors have the same direction.
05

Summarize the orientation of velocity and acceleration vectors

To answer the exercise, we have analyzed the orientation of the velocity and acceleration vectors throughout the ball's flight: 1. During the upward flight, the velocity vector points upward while the acceleration due to gravity points downward. They have opposite directions. 2. At the highest point, the velocity vector is momentarily zero (no direction) while the acceleration due to gravity is still downward. 3. During the downward flight, both the velocity and acceleration vectors point downward. They have the same direction.

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Most popular questions from this chapter

The trajectory of an object is given by the equation $$ x(t)=(4.35 \mathrm{~m})+(25.9 \mathrm{~m} / \mathrm{s}) t-\left(11.79 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2} $$ a) For which time \(t\) is the displacement \(x(t)\) at its maximum? b) What is this maximum value?

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