Question

A squirrel sitting on a peak of a roof which is 1.50 m above the bottom of the roof and 4.50 m above the ground puts an acorn on the roof. It starts from rest at the peak and slides down the sloped roof (coefficient of friction = 0.150) which is angled at 25.0 degrees to the horizontal. After the acorn reaches the edge of the roof it flies off and becomes a projectile. You may ignore air resistance. Part A what is the acorn's acceleration as it slides down the rood? PArt B Find the velocity of the acorn at the edge of the roof? Part C How long after the acorn left the roof does is hit the ground? PArt E How far from the side of the house does the acorn hit the ground?

Answer 1

Here,
Height of peak of roof = 1.5 m
Height of roof from ground = 4.5 m

Part A:
Wriitng Diffrent forces in components we get
F + mgsin25-Ff = -------------------(1)
N = mgCos25 --------------(2)
also,
as we know Frictional Force Ff is Equal to:
Ff = uN

Therefore,eqn 1 becomes
F = -mgSin25 + u*mgCos25
ma = -mgSin25 + u*mgCos25
a = g(-sin25 + ucos25)
a = 9.8*(-0.42 + 0.150*0.90)
a = -2.793 m/s^2

The Acceleration of acorn as it slide's Down is -2.793 m/s^2

Part B:
Kinetic Energy at edge of roof = Potential Energy at edge roof
1/2 * m * V^2 = m * g * h
V =sqrt(2 * g * h)
V = sqrt(2*9.8*4.5)
V = 9.39 m/s

the velocity of the acorn at the edge of the roof 9.39 m/s

PartC:
as now acorn is in projectile Motion so,
Time of Fight = T = 2V/g
T = 2*9.39/9.8
T = 1.916 s nearly equal to 2s

Total time taken by Acorn before hitting the ground is 1.916s or 2s approx

Part E:
from projectile motion, total range of flight is given by
R = v^2/g
R = 9.39^2 / 9.8
R = 8.99 m

Total distance travelled by acorn before hitting the ground from the wall is 8.99m