Question

Two identical cars collide at an intersection(m=1500kg). Car 1 is traveling east with a speed of 16 m/s and car 2 is traveling north with a speed of 12 m/s. Immediately after the collison, car 1 travels with a speed of 8 m/s in a direction 60 north of east. The cars do not stick together.

(a) What is the speed and direction of travel for car 2 after the collision? (b) What is the change in kinetic energy of the 2 car system?

Answer 1

here,

mass of each car , m = 1500 kg

initial speed of 1 , u1 = 16 m/s i

initial speed of 2 , u2 = 12 j m/s

final speed of 1 , v1 = 8 *( cos(60) i + sin(60) j)

v1 = 4 i m/s + 6.9 j m/s

let the final speed of 2 be v2

using conservation of momentum

m * u1 + m * u2= m * v1 + m * v2

16 i + 12 j = 4 i + 6.9 j + v2

v2 = 12 i + 5.1 j m/s

a)

the speed of car 2, |v2| = sqrt(12^2 + 5.1^2) = 13.1 m/s

the direction , theta = arctan(5.1/12) = 23 degree North of east

b)

the change in kinetic energy of the 2 car system , dKE = (0.5 * m * v1^2 + 0.5 * m * v2^2) - ( 0.5 * m * u1^2 + 0.5 * m * u2^2)

dKE = 0.5 * 1500 * ( 13.1^2 + 8^2 - 16^2 -12^2 )

dKE = - 1.23 * 10^5 J