23.0k views
3 votes
A ball is projected upward at time t = 0.0 s. from a point on a roof 90 m above the ball rises, then falls and strikes the ground. The initial velocity of the ball is 36.2 m/s if air resistance is negligible. (a) What is the maximum height the ball can reach? (b) Calculate the time when the ball strikes the ground? (c) How fast will it be moving just before it hits the ground?

User UML GURU
by
7.8k points

1 Answer

7 votes

Final answer:

The maximum height the ball can reach is 65.75 m. The ball will strike the ground approximately 3.696 seconds after being projected upward. The ball will be moving at approximately -0.247 m/s just before it hits the ground.

Step-by-step explanation:

To solve this problem, we can use the equations of motion for a projectile. Since the initial velocity is only in the vertical direction, we can separate the motion into vertical and horizontal components.

(a) Maximum height:

The maximum height can be found using the equation:

vf^2 - vi^2 = 2ad

Where vf is the final velocity (0 m/s at the maximum height), vi is the initial velocity (36.2 m/s), a is the acceleration (-9.8 m/s^2), and d is the displacement in the vertical direction (the maximum height).

By substituting the known values into the equation, we can solve for d:

0 - (36.2)^2 = 2*(-9.8)*d

d = 65.75 m

Therefore, the maximum height the ball can reach is 65.75 m.

(b) Time to strike the ground:

The time it takes for the ball to strike the ground can be calculated using the equation:

t = (vf - vi) / a

Where vf is the final velocity (0 m/s), vi is the initial velocity (36.2 m/s), and a is the acceleration (-9.8 m/s^2).

By substituting the known values into the equation, we can solve for t:

t = (0 - 36.2) / (-9.8)

t ≈ 3.696 s

Therefore, the ball strikes the ground approximately 3.696 seconds after being projected upward.

(c) Velocity just before hitting the ground:

The velocity just before the ball hits the ground can be calculated using the equation:

v = vi + a*t

Where v is the final velocity, vi is the initial velocity (36.2 m/s), a is the acceleration (-9.8 m/s^2), and t is the time to strike the ground (3.696 s).

By substituting the known values into the equation, we can solve for v:

v = 36.2 + (-9.8)*3.696

v ≈ -0.247 m/s

Therefore, the ball will be moving at approximately -0.247 m/s just before it hits the ground.

User Alvin Sartor
by
7.7k points