**Problem:**A ball is thrown up in the air with an initial velocity of 21 m/s upward. How long does it take the ball to return to the ground? _______ sec.**Solution:**To solve this problem, we need to find the total time for the ball to go up and come back down. We'll use kinematic equations for motion under gravity.Stages of motion:1. **Ascent:** The ball rises until its velocity becomes zero.2. **Descent:** The ball falls back to the ground.**Given Data:**- Initial velocity (\(v_i\)) = 21 m/s (upward)- Acceleration due to gravity (\(g\)) = 9.8 m/s² (downward)**Step 1: Calculate time to reach the highest point**The time (\(t_{up}\)) it takes to reach the highest point is when the final velocity (\(v_f\)) is 0 m/s:\[v_f = v_i - gt_{up}\]\[0 = 21 - 9.8t_{up}\]\[9.8t_{up} = 21\]\[t_{up} = \frac{21}{9.8} \approx 2.14 \text{ sec}\]**Step 2: Calculate total time for round trip**The time to ascend and descend is the same. Therefore, the total time (\(t_{total}\)) is:\[t_{total} = 2 \times t_{up} \approx 2 \times 2.14 = 4.28 \text{ sec}\]Thus, the ball takes approximately **4.28 seconds** to return to the ground.

Given data: Initial velocity (V0) = 21 m/s, upward direction Required: The time taken to return to…

Answered: A ball is thrown up in the air with an…

A ball is thrown up in the air with an initial velocity of 21 m/s upward. How long does it take the ball to return to the ground? sec.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Problem:**

A ball is thrown up in the air with an initial velocity of 21 m/s upward. How long does it take the ball to return to the ground? _______ sec.

**Solution:**

To solve this problem, we need to find the total time for the ball to go up and come back down. We'll use kinematic equations for motion under gravity.

Stages of motion:
1. **Ascent:** The ball rises until its velocity becomes zero.
2. **Descent:** The ball falls back to the ground.

**Given Data:**
- Initial velocity (\(v_i\)) = 21 m/s (upward)
- Acceleration due to gravity (\(g\)) = 9.8 m/s² (downward)

**Step 1: Calculate time to reach the highest point**

The time (\(t_{up}\)) it takes to reach the highest point is when the final velocity (\(v_f\)) is 0 m/s:
\[
v_f = v_i - gt_{up}
\]
\[
0 = 21 - 9.8t_{up}
\]
\[
9.8t_{up} = 21
\]
\[
t_{up} = \frac{21}{9.8} \approx 2.14 \text{ sec}
\]

**Step 2: Calculate total time for round trip**

The time to ascend and descend is the same. Therefore, the total time (\(t_{total}\)) is:
\[
t_{total} = 2 \times t_{up} \approx 2 \times 2.14 = 4.28 \text{ sec}
\]

Thus, the ball takes approximately **4.28 seconds** to return to the ground.

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