Question

A person is at the top of a mountain. Throw a ball straight up with unknown speed. the ball reaches the maximum height of 490 meters (measured from the base of the mountain). It also took 12.5 seconds for the ball to reach the base of the mountain. Determine the initial speed of the ball, and what is the height of the mountain.

Answer 1

here,

let the initial speed of ball be u and height of mountain be h0

the maximum height , hm = h0 + (u^2 /(2g))

490 = h0 + (u^2 /(2*9.81)) ......(1)

and

for vertical direction

- h0 = u * t - 0.5 * g * t^2

- h0 = u * 12.5 - 0.5 * 9.81 * 12.5^2 .....(2)

from (1) and (2)

h0 = 459.3 m

u = 24.6 m/s

the height of mountain is 459.3 m

the initial speed of ball is 24.6 m/s