A student kicks a football vertically upwards, causing the football to reach a maximum height of 40.0m before falling back to the ground. Determine all unknowns and answer the following questions. Neglect drag and the initial height and horizontal motion of the football. A) With what speed was the football kicked?
B) What was the football's total flight time?

A. 28 m/s

B. 5.72 s

Explanation:

The following data were obtained from the question:

Maximum height (h) = 40 m

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

A. Determination of the initial velocity.

Maximum height (h) = 40 m

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

Velocity at maximum height (v) = 0 m/s

Initial velocity (u) =.?

v² = u² – 2gh (Ball is going against gravity)

0² = u² – (2 × 9.8 × 40)

0 = u² – 784

Collect like terms

0 + 784 = u²

784 = u²

Take the square root of both side

u = √784

u = 28 m/s

Thus, the ball was kicked with a velocity of 28 m/s

B. Determination of the time of flight.

We'll begin by calculating the time taken to reach the maximum height. This can be obtained as follow:

Velocity at maximum height (v) = 0 m/s

Initial velocity (u) = 28 m/s

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

v = u – gt (Ball is going against gravity)

0 = 28 – 9.8t

Rearrange

0 + 9.8t = 28

9.8t = 28

Divide both side by 9.8

t = 28/9.8

t = 2.86 s

Finally, we shall determine the the time of flight as follow:

Time taken to reach the maximum height (t) = 2.86 s

Time of flight (T) =?

T = 2t

T = 2 × 2.86

T = 5.72 s

Therefore, the time of flight for the ball is 5.72 s

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