Question

A 1000-kg car moving north with a speed of 25.0 m/s collides with a 2000- kg truck moving at an angle of 30° north of west with a speed of 20.0 mjs. After the collision, the car and the truck stuck together. What is the magnitude of their common velocity after the collision?

Answer 1

here,

mass of car , m1 = 1000 kg

mass of truck , m2 = 2000 kg

initial speed of car , u1 = 25 m/s j

initial speed of truck , u2 = 20 m/s * ( - cos(30) i + sin(30) j)

u2 = - 17.33 i m/s + 10 j m/s

let the common velocity after the collison be v

using conservation of momentum

m1 * u1 + m2 * u2 = (m1 + m2) * v

1000 * 25 j + 2000 * ( - 17.33 i + 10 j) = ( 1000 + 2000) * v

solving for v

v = 11.56 i m/s + 5 j m/s

the magnitude of their common velocity after the collision, |v| = sqrt(11.56^2 + 5^2)

|v| = 12.6 m/s