# Homework #3 Solutions

HOMEWORK #3

Due Monday July 2, 2012

1

James Bond (90 kg), outﬁtted with perfectly matching skis and skiware, is at the top of a steep slope that a secret spy like him can easily handle. He lets himself go from rest and smoothly slides down the h = 15 m high hill. A big parking lot lies at the bottom of the hill. Since the parking area has been cleared of snow, the friction between the ground and the skis brings our hero to a halt at point D, located at a distance d = 12 m from point C. The descent can be considered frictionless. Take the potential energy to be zero at the bottom of the slope. (a) What is the mechanical energy of James Bond at points A and D? (b) Determine the speed of Bond at position B

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(a) Estimate the total impulse on the ball. (b) Estimate the velocity of the ball after being struck, assuming the ball is (-) being served, so it is nearly at rest initially. (-) moving perpendicularly toward the racquet at 10.0 m/s. (-) moving at 10.0 m/s and hitting the racquet at an angle of 45.0◦ . SOLUTION : (a) The impulse is equal to the area under the force curve with rexpect to the x-axis: J= F dt

= (number of squares × area of a square)ˆ ı = 40 (0.001 s) (25 N)ˆ = 1.0 N s ˆ ı ı (b) Let us express the ﬁnal velocity in terms of the impulse, mass and the initial velocity. We take the positive direction to be away from the racquet. J = ∆p = m (vf − v0 ) (−)v0 = 0 (−)v0 = −10.0 m/s J + v0 m 1.0 N s ˆ + 0 = 16.7 m/s ˆ ı ı ⇒vf = 0.060 kg 1.0 N s ˆ − 10.0 m/s ˆ = 6.7 m/s ˆ ⇒vf = ı ı ı 0.060 kg ⇒vf =

For the last case, we need to ﬁnd the perpendicular and tangentional components of the ball’s velocity. Since the impulse is only perpendicular to the plane of the racquet, only the perpendicular component of