A ball is thrown horizontally at 30 m/s from a height of 45m. How long is it in the air? (i) How fast is it moving horizontally when it hits the ground?

1.25s

1) 90.9m

Explanation:

From the question, we are given the following;

Speed v = 30m/s

Maximum height H = 45m

Required;

Time

Using the equation of motion S = ut + 1/2gt²

Substitute;

45= 30t + 1/2(9.8)t²

45 = 30t + 4.9t²

4.9t² + 30t - 45 = 0

Factorize;

t = -30 ±√30²-4(-45)(4.9)/2(4.9)

t = -30 ±√900+882/9.8

t = -30 ±42.21/9.8

t = -30 + 42.21/9.8

t = 12.21/9.8

t = 1.25secs

Hence the ball spent 1.25secs in air.

i) To get the horizontal distance, we will use the formula;

R = U√2H/g

R = 30√2(45)/9.8

R = 30√90/9.8

R = 30√9.18

R = 30(3.03)

R = 90.9m

Hence the horizontal distance is 90.9m

the duration of a photographic flash is related to an rc time constant, which is 0.100 μs for a certain camera.