If you throw a ball straight upward at a speed of 11 m/s, How long will it take to return to its starting point?

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To determine how long it will take for the ball to return to its starting point, we need to use the concept of free fall motion and consider the effects of gravity. Here's how you can calculate it:

1. Identify the given information:
- Initial velocity (u) = 11 m/s (upward)
- Final velocity (v) = ? (when the ball returns to its starting point)
- Acceleration due to gravity (a) = -9.8 m/s² (since the ball is moving upward, acceleration is negative)

2. Use the equation of motion for vertical displacement:
v² = u² + 2as

Since the ball returns to its starting point, the final displacement (s) is zero. Therefore, the equation becomes:
0 = (11 m/s)² + 2(-9.8 m/s²)(s)

3. Rearrange the equation to solve for the final velocity (v):
v = √((11 m/s)² + 2(-9.8 m/s²)(s))

4. As the ball reaches its maximum height, the final velocity becomes zero. So substitute v = 0 into the equation:
0 = (11 m/s)² + 2(-9.8 m/s²)(s)

5. Solve for the displacement (s):
s = (11 m/s)² / (2(-9.8 m/s²))

6. Now, we know that the time it takes for the ball to reach its maximum height (t₁) is given by:
v = u + at₁
0 = 11 m/s - 9.8 m/s²(t₁)

Solve for t₁:
t₁ = 11 m/s / 9.8 m/s²

7. Since the total time of ascent and descent is twice the time of ascent (t₁), the total time (t) it takes for the ball to return to its starting point is:
t = 2 * t₁

8. Substitute the value of t₁ into the equation to find the total time (t).

By following these steps, you can calculate the total time it takes for the ball to return to its starting point.

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