A snowball rolls off a barn roof that slopes downward at an angle of ? = 40°. Th

Question

A snowball rolls off a barn roof that slopes downward at an angle of ? = 40°. The edge of the roof is h = 11.5 m above the ground, and the snowball has a speed of v0 = 6.50 m/s as it rolls off the roof. Ignore air resistance.

(a) How far from the edge of the barn does the snowball strike the ground if it doesn't strike anything else while falling?

(b) A man 1.9 m tall is standing 4.0 m from the edge of the barn. Will he be hit by the snowball?

(c) How far from the edge of the barn is the snowball when it is at the same height as the man?

Explanation / Answer

a)initial velocity is 6.50 m/s below 40 deg.

in vertical it have to travel 11.5 m to reach the groundd.

y = -11.5 m

uy = -6.5sin40 = -4.18 m/s

a = -9.81m/s^2

applying, y = uy*t + at^2/2

- 11.5 = - 4.18t - 9.81t^2/2

t = 1.16 sec

In horizontal,

Dx = ux *t = (6.50 cos40) 1.16 = 5.78 m ...Ans

(B) time taken to reach 4m horiozontally.

4 = 6.50cos40 t

t = 0.803 sec

y = (6.50sin40)*0.803 + 9.81(0.803^2)/2

y = 6.51 m

height from ground.

h = 11.5 - 6.51 = 4.98 m

so ball will not hit.

(c) time taken to travel = 11.5 - 1.9 = 9.6m is t then

9.6 = (6.5 sin40)t + 9.81t^2/2

t = 1.04 sec

Horiozontal distance = 6.50cos40 * 1.04 = 5.18 m

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