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A ball is tossed with enough speed straight up so that it

Chapter 3, Problem 2P

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QUESTION:

A ball is tossed with enough speed straight up so that it is in the air several seconds.

(a) What is the velocity of the ball when it reaches its highest point?

(b) What is its velocity 1 s before it reaches its highest point?

(c) What is the change in its velocity during this 1-s interval?

(d) What is its velocity 1 s after it reaches its highest point?

(e) What is the change in velocity during this 1-s interval?

(f) What is the change in velocity during the 2-s interval? (Careful!)

(g) What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity?

Questions & Answers

QUESTION:

A ball is tossed with enough speed straight up so that it is in the air several seconds.

(a) What is the velocity of the ball when it reaches its highest point?

(b) What is its velocity 1 s before it reaches its highest point?

(c) What is the change in its velocity during this 1-s interval?

(d) What is its velocity 1 s after it reaches its highest point?

(e) What is the change in velocity during this 1-s interval?

(f) What is the change in velocity during the 2-s interval? (Careful!)

(g) What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity?

ANSWER:

Step 1 of 3

(a)

When a ball is thrown vertically upward, its velocity decreases due to the acceleration of gravity until it reaches its highest point. At the highest point, the velocity becomes zero before it starts to descend. This is because at the highest point, the ball momentarily comes to a stop before gravity starts pulling it back down.

\(v = 0\)

(b)

The ball’s velocity \(1\;{\rm{s}}\) before it reaches its highest point is,

\(v = {v_1} + at\)

\(0 = {v_1} + \left( { - g} \right)t\)

\({v_1} = gt\)

Here, \(g\) is the acceleration due to gravity having an approximately value of \(10\;\frac{{\rm{m}}}{{{{\rm{s}}^2}}}\).

Plug the value of \(10\;\frac{{\rm{m}}}{{{{\rm{s}}^2}}}\) for \(g\), and \(1\;{\rm{s}}\) for \(t\) in the above equation.

\({v_1} = 10 \times 1\)

\( = 10\;\frac{{\rm{m}}}{{\rm{s}}}\)

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