1. A driver is traveling on dry pavement at a high rate of speed when she spots
ID: 1880981 • Letter: 1
Question
1. A driver is traveling on dry pavement at a high rate of speed when she spots a deer in the road. She slams on her brakes and locks up the wheels, going into a skid, and manages to stop just before striking the deer. (a) If she was traveling 35 mph, how far away was the deer when she hit the brakes? (b) Repeat part (a) but with the assumption that the car had had antilock brakes that limit the wheel torque so that it is slightly below the skid threshold. For both (a) and (b) take s = 0:7 for the wheels/pavement, and k to be 0.4.
4. A child riding in the car described in problem (1) is holding a helium balloon by a string when the deer is spotted. The string is short enough so that balloon does not touch the ceiling. During the deceleration, will the balloon drift towards the back of the car, or towards the front of the car? Assuming that there is time during the skid for the balloon to come to a new equilibrium, what angle will the string make with the vertical in (a)? What will be the angle during the deceleration described (b)?
Explanation / Answer
Given that,
lnitial speed, u = 35 mph = 15.6 m/s
Final speed, v = 0
acceleration, a = -uk*g
a = -0.4*9.8 = -3.92 m/s^2
From kinematic equation,
v^2 - u^2 = 2as
0 - (15.6)^ = -2*3.92*s
s = 31 m
(b)
Wen antilock brakes are applied,
a = -us*g
a = -0.7*9.8 = -6.86 m/s^2
v^2 - u^2 = 2as
0 - (15.6)^2 = -2*6.86*s
s = 17.7 m
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