Problem 3- Projectile Motion A ball is thrown from the ground to the top of a bu

Question

Problem 3- Projectile Motion A ball is thrown from the ground to the top of a building with a height of h 29.4 m, The initial velocity is vo 36.6m/s and the angle between the ground and Vo is a- 62. a) After how many seconds does the ball land on the roof of the building? (10 points) b) What are the values of the horizontal and vertical components of the ball's velocity just before the ball hits the roof? What is the magnitude of the velocity at that same moment? (10 points) o) What is the maximum height H with respect to the ground which is reached by the ball? (10 points) Do not consider air resistance throughout the problerm. ci

Explanation / Answer

net Force F = F thrust - Fk

net force = ma

Fk = uk mg

where uk beign Coefficient of kinetic friction

then from net force

ma = Fthrust - uk mg

accleration a = (F thrust - uk mg)/m

part A "

time of flight Tf = 2 u sin theta/g

Tf = (2 * 36.6 * sin 62)/(9.81

Tf = 6.58 sec

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before hitting the roof

vertical Component of velocuty Vy = V sin theta

Vy = 36.6 * sin 62

Vy = 32.31 m/s

Horizontal component Vx = V cos thrta

Vx = 36.6 * cos 62

Vx = 17.18 m/s

magnitude of V = sqrt(vx^2 + Vy^2)

V^2 = 32.31^2 + 17.18^2

V = 36.6 m/s

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Hmax = u^2 sin^2 theta/2g

Hmax = (36.6*36.6* sin 62* sin 62)/(2* 9.81)

Hamx = 53.2 m

total height frim ground = 53.2 + 29.4 = 82.62 m

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