You throw a ball straight up. You are extra strong feeling today. It takes 11 seconds for the ball to come back down. a. How high did you throw it?
b. What was the initial speed you threw it at?

A. 148.23 m

B. 2.75 m/s

Explanation:

The following data were obtained from the question:

Time of flight (T) = 11 s

Maximum height (h) =?

Initial velocity (u) =?

Next, we shall determine the time taken for the ball to get to the maximum height. This can be obtained as follow:

Time of flight (T) = 11 s

Time (t) to reach the maximum height =.?

T = 2t

11 = 2t

Divide both side by 2

t = 11/2

t = 5.5 s

NOTE: Time to reach the maximum height is the same as the time taken for the ball to fall back to the plane of projection.

A. Determination of the maximum height to which the ball was thrown.

Time (t) to reach maximum height = 5.5 s

Acceleration due to gravity (g) = 9.8 m/s²

Maximum height (h) =?

h = ½gt²

h = ½ × 9.8 × 5.5²

h = 4.9 × 30.25

h = 148.23 m

B. Determination of the initial velocity.

Maximum height (h) reached = 148.23 m

Acceleration due to gravity (g) = 9.8 m/s²

Initial velocity (u) =?

u² = h/2g

u² = 148.23 / (2 × 9.8)

u² = 148.23 / 19.6

Take the square root of both side

u = √(148.23 / 19.6)

u = 2.75 m/s

true tan speed = ang vel x radius