Question

A ball is thrown with a speed of 20m/s at an angle of 87° above tge horizontal. It lands on the roof of a building at a point displaced 24m horizontally from the throwing point. How high above the throwing point is the roof?

Answer 1

Correct question:

A ball is thrown with a speed of 20m/s at an angle of 37° above the horizontal. It lands on the roof of a building at a point displaced 24m horizontally from the throwing point. How high above the throwing point is the roof?

Reason for correction:

If the angle is 87° then the horizontal range is 4.16m it can never reach a distance of 24m. Most of the questions involve angles 37° or 53°. So I have chosen 37°

Answer:

6.75m

Explanation:

Given,

• A ball is thrown with a speed of 20m/s at an angle of 37° above the horizontal.
• It lands on the roof of a building at a point displaced 24m horizontally from the throwing point.

Known parameters:

u = 20m/s;

ux = intial horizontal velocity = ucosø = 16m/s

uy = intial vertical velocity = usinø = 12m/s

X = 24m

W.K.T, s = ut + at²/2

For horizontal motion of projectile, u = ux, a = 0

X = uxt

t = X/ux

t = 24/16

t = 1.5s

For vertical motion of projectile, u = uy, a = -g

Y = uyt - gt²/2

Y = 12(1.5) - 10(1.5)²/2

Y = 18 - 5(2.25)

Y = 18 - 11.25

Y = 6.75m

Height of roof = 6.75m