Question

A 800-kg sports car collides into the rear end of a 2900-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.9 m before stopping. The police officer, estimating the coefficient of kinetic friction between tires and road to be 0.80, calculates the speed of the sports car at

Answer 1

consider the motion of combination after collision

a = acceleration = - u_k g = - 0.80 x 9.8 = - 7.84 m/s²

d = stopping distance = 2.9 m

v_i = initial speed after collision = ?

v_f = final speed = 0 m/s

using the equation

v_f² = v_i² + 2 a d

0² = v_i² + 2 (- 7.84) (2.9)

v_i = 6.74 m/s

m = mass of sports car = 800 kg

M = mass of SUV car = 2900 kg

v = speed of sports car before collision = ?

V = speed of SUV car before collision = 0

Using conservation of momentum

mv + M V = (m + M) v_i

800 v + (2900) (0) = (800 + 2900) (6.74)

v = 31.2 m/s