Question

A 1200-kg car is moving at 16.0 m/s due north. A 1500-kg car is moving at 20.0 m/s due east. The two cars simultaneously approach an icy intersection where, with no brakes or steering, they collide and stick together.

1)

Determine the speed of the combined two-car wreck immediately after the collision. (Express your answer to two significant figures.)

m/sm/s

2)

Determine the direction of the combined two-car wreck immediately after the collision. (Express your answer to two significant figures.)

Answer 1

1)

Assume north-south direction along y-axis and east-west direction along x-axis

m₁ = mass of the car moving due north = 1200 kg

v_1i = initial velocity of car moving due north = 0 i + 16 j

m₂ = mass of the car moving due east = 1500 kg

v_2i = initial velocity of car moving due east = 20 i + 0 j

v = final velocity after collision

Using conservation of momentum

m₁ v_1i + m₂ v_2i = (m₁ + m₂) v

(1200) (0 i + 16 j) + (1500) (20 i + 0 j) = (1200 + 1500) v

30,000 i + 19200 j = 2700 v

v = 11.11 i + 7.11 j

Speed of the wreck using Pythagorean theorem is given as

|v| = speed = sqrt((11.11)² + (7.11)²) = 13.2 m/s

b)

$\theta$ = direction = tan^-1(7.11/11.11) = 33 deg