Ch4 #63 A car is parked on a steep incline, making an angle of 37.0 degree below
ID: 2164061 • Letter: C
Question
Ch4 #63
A car is parked on a steep incline, making an angle of 37.0 degree below the horizontal and overlooking the ocean, when its brakes fail and it begins to roll. Starting from rest at t = 0, the car rolls down the incline with a constant acceleration of 4.00 m/s2, traveling 50.0 m to the edge of a vertical cliff. The cliff is 30.0 in above the ocean. Find the speed of the car when it reaches the edge of the cliff, the time interval elapsed when it arrives there, the velocity of the car when it lands in the ocean, the total time interval the car is in motion, and the position of the car when it lands in the ocean, relative to the base of the cliff.Explanation / Answer
S = 1/2 a t1^2 for car rolling t1 = (2 * 50 / 4)^1/2 = 5 sec to reach cliff V = a t1 = 4 * 5 = 20 m/s at edge of cliff Vx = 20 cos 37 = 16.0 m/s Vy = 12.0 m/s 30 = Vy t + 1/2 g t^2 for vertical fall of car Solve quadratic for t to get time of fall Sx = Vx t using value of t just found This gives you the position of the car Vyf = Vy + g t final vertical speed of car V = (Vx^2 + Vyf^2)^1/2 final speed of car tan theta = Vyf / Vx angle of car from vertical