Question

the shape of sugarloaf mt. in rio de janeiro, brazil is such that if you were to kick a soccer ball hard enough, it could land near the base of the mountain without hitting the mountain's side. Suppose the ball is kicked horizontally with an initial speed of 9.37 m/s. if the ball travels horizontal distance of 85.0 m, how tall is the mountain?

Answer 1

The ball is in the air
T = (85 m)/9.37 m/s) = 9.1 s

Calculate how far it falls in that time. That will be the mountain height,

H = (g/2) T^2

This agrees with the formula given by JOHNNY

You will be ignoring air resistance, which is NOT a good assumption for a soccer ball travelling that far and fast. It will probably nearly reach a terminal velocity and quit accelerating

Answer 2

jdx

Answer 3

404m