a ball is thrown vertically upward with a speed 25.0m/s (a)How high does it rise? (b)How long does it take to reach its highes point? (c)How long does it take to hit the ground after it reaches its highest point? (d)What is its speed when it returns to the level from which it started?

To find the answers to these questions, we can use the equations of motion for vertical motion under constant acceleration (in this case, due to gravity). The following information will be useful:

Initial velocity, u = 25.0 m/s (upward)
Final velocity, v = ?
Acceleration, a = -9.8 m/s^2 (downward)
Displacement, s = ?
Time, t = ?

(a) How high does it rise?

To find the height, we need to determine the maximum point the ball reaches. At the highest point, the ball momentarily comes to rest before it starts to fall downwards. Therefore, the final velocity (v) at the highest point is 0 m/s.

Using the equation v^2 = u^2 + 2as and rearranging it to solve for 's':

0^2 = (25.0)^2 + 2(-9.8)s

Solving for 's', we get:

s = (25.0)^2 / (2 * 9.8)

Plugging in the values, we find:

s ≈ 31.88 meters

So, the ball rises approximately 31.88 meters.

(b) How long does it take to reach its highest point?

To find the time taken to reach the highest point, we can use the equation v = u + at, where v = 0 m/s.

0 = 25.0 + (-9.8)t

Solving for 't', we get:

t = 25.0 / 9.8

Plugging in the values, we find:

t ≈ 2.55 seconds

So, it takes approximately 2.55 seconds to reach the highest point.

(c) How long does it take to hit the ground after it reaches its highest point?

The time taken to hit the ground after reaching the highest point is the same as the time taken to reach the highest point but in reverse. So, it will also be approximately 2.55 seconds.

(d) What is its speed when it returns to the level from which it started?

To find the speed when the ball returns to the level from which it started, we can use the equation v = u + at.

Substituting the known values, we have:

v = 25.0 - 9.8 * 2.55

Simplifying, we find:

v ≈ -2.05 m/s

The negative sign indicates that the ball is moving downward. Therefore, the speed when it returns to the starting level is approximately 2.05 m/s downward.