Question

A 1060-kg car moving west at 16 m/s collides with and locks onto a 1830-kg stationary car. determine the velocity of the cars just after the collision.

Answer 1

Using the conservation of momentum, the velocity of the cars just after an inelastic collision where a 1060-kg car moving west at 16 m/s collides with and locks onto a 1830-kg stationary car, is calculated to be approximately 5.87 m/s west.

Step-by-step explanation:

To determine the velocity of the cars just after the collision, we can use the principle of conservation of momentum. Since the cars lock together after the collision, it is an inelastic collision, and momentum is conserved. The total momentum before the collision must equal the total momentum after the collision.

We have:

Mass of car 1 (m1): 1060 kg

Velocity of car 1 (v1): 16 m/s west

Mass of car 2 (m2): 1830 kg (stationary)

Velocity of car 2 (v2): 0 m/s

The combined mass after the collision is m1 + m2.

The momentum before the collision for car 1 is m1 × v1.

Since momentum is conserved:(m1 × v1) + (m2 × v2) = (m1 + m2) × velocity after collision

Plugging in the values: 1060 kg × 16 m/s + 1830 kg × 0 m/s = (1060 kg + 1830 kg) × velocity after collision

16960 kg·m/s = 2890 kg × velocity after collision

The velocity after the collision is: 16960 kg·m/s / 2890 kg ≈ 5.87 m/s west

Answer 2

M1U1 + M2V2 = (M1+M2)V, where M1 is the mass of the moving car, M2 is the mass of the stationary car, U1 is the initial velocity, and V is the common velocity after collision.
therefore;
(1060× 16) + (1830 ×0) = (1060 +1830) V
16960 = 2890 V
V = 5.869 m/s
The velocity of the cars after collision will be 5.689 m/s