if you throw a ball straight upward at a speed of 10 m/s, how long will it take to reach zero speed? how long will take to return to its starting point? how fast will it be going when it returns to its sparting point?

To answer these questions, we'll need to use some physics equations and concepts. Specifically, we'll be using the equations of motion for an object moving vertically under constant acceleration due to gravity.

The equation we'll use here is:

vf = vi + at

where:
- vf is the final velocity
- vi is the initial velocity
- a is the acceleration
- t is the time

Let's break down each question and calculate the answers step by step:

1. How long will it take to reach zero speed?
When the ball reaches its maximum height, its velocity will momentarily become zero before it starts falling back down. At that point, the final velocity (vf) will be zero, the initial velocity (vi) will be 10 m/s (given), and the acceleration (a) will be -9.8 m/s² (negative because the ball is moving upwards against the force of gravity).

Plugging these values into the equation, we get:

0 = 10 - 9.8t

Rearranging the equation, we find:

9.8t = 10

t = 10 / 9.8
t ≈ 1.02 seconds

So it will take approximately 1.02 seconds for the ball to reach zero speed.

2. How long will it take to return to its starting point?
To calculate the total time it takes for the ball to return to its starting point, we need to consider both the upward and downward motion. The time it takes for the ball to reach its maximum height is half of the total time of the entire motion.

Using the equation of motion:

vf = vi + at

When the ball reaches the maximum height, its final velocity is zero, initial velocity is 10 m/s, and acceleration is -9.8 m/s². Plugging these values in:

0 = 10 - 9.8t

t = 1.02 seconds

Since the ball takes 1.02 seconds to reach its maximum height, it will also take 1.02 seconds to fall back down. Therefore, the total time to return to its starting point is:

1.02 + 1.02 = 2.04 seconds

So, it will take approximately 2.04 seconds for the ball to return to its starting point.

3. How fast will it be going when it returns to its starting point?
To determine the velocity at the starting point, we can use the equation:

vf = vi + at

In this case, the final velocity (vf) will be the velocity at the starting point, the initial velocity (vi) will be 10 m/s (given), the acceleration (a) will be -9.8 m/s² (due to gravity), and the time (t) will be 2.04 seconds (as calculated in the previous question).

Plugging these values into the equation, we have:

vf = 10 - 9.8 * 2.04

vf ≈ -9.99 m/s

The negative sign indicates that the ball is moving downwards. Therefore, when the ball returns to its starting point, it will be traveling at approximately 9.99 m/s downward.

So, the ball will be going approximately 9.99 m/s downward when it returns to its starting point.

tsees