One side of the roof of a building slopes up at 38.0°. A roofer kicks a round, f

Question

One side of the roof of a building slopes up at 38.0°. A roofer kicks a round, flat rock that has been thrown onto the roof by a neighborhood child. The rock slides straight up the incline with an initial speed of 15.0 m/s. The coefficient of kinetic friction between the rock and the roof is 0.470. The rock slides 10.0 m up the roof to its peak. It crosses the ridge and goes into free fall, following a parabolic trajectory above the far side of the roof, with negligible air resistance. Determine the maximum height the rock reaches above the point where it was kicked.
( m)

Explanation / Answer

given, initial speed, vo = 15 m/s
angle of incline, theta = 38 deg
coefficient of kinetic firction, k = 0.47
distance travelled along the incline, d = 10 m

so, initial KE = 0.5mvo^2 ( assuming m to be the mass of the object)
Friction torce = k*mg*cos(theta)
Energy lost to friction = k*mg*d*cos(theta)
PE gained = mg*d*sin(theta)
so, let final velocity be u
then from conservation of energy
0.5mu^2 + mgdsin(theta) + k*mg*d*cos(theta)= 0.5mvo^2
u^2 + 2g*10*sin(38) + 2*0.47*g*10*cos(38)= 15^2
u = 5.61 m/s

so the rock gets launched like a projectile from top of the roof at an angle theta, initial speed, u = 5.61 m/s
so maximum height above the point in was kicked = d(sin(theta)) + h
where 0.5mu^2 = mgh
h = 0.5*5.61^2/9.81 = 1.604 m
so total height = 10*sin(38) + h = 7.7606 m

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.