A 1000-kg car moving at 80 km/h collides head on with a 100-kg car moving west at 40km/h, and the two cars stick together. Which way does the wreckage move and with what initial speed?
Use conservation of momentum:
1000*80-100*40=1110(V)
solve for V. postive means East.
3.6 m/s^2
To solve this problem, we can apply the principle of conservation of momentum. Momentum is the product of mass and velocity, and according to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Let's assign directions to the velocities. Since the 1000-kg car is moving head-on, its velocity will be positive, and the 100-kg car moving west will have a negative velocity. We'll consider the positive direction as the direction in which the 1000-kg car is moving.
Given:
Mass of the 1000-kg car (m1) = 1000 kg
Velocity of the 1000-kg car (v1) = 80 km/h
Mass of the 100-kg car (m2) = 100 kg
Velocity of the 100-kg car (v2) = -40 km/h
Step 1: Convert the velocities from km/h to m/s.
v1 = 80 km/h × (1000 m/3600 s) = 22.22 m/s
v2 = -40 km/h × (1000 m/3600 s) = -11.11 m/s
Step 2: Calculate the total momentum before the collision.
p_initial = m1 * v1 + m2 * v2
p_initial = (1000 kg × 22.22 m/s) + (100 kg × -11.11 m/s)
p_initial = 22220 kg·m/s - 1111 kg·m/s
p_initial = 21109 kg·m/s
Step 3: Since the two cars stick together after the collision, their combined mass can be used to calculate the final velocity.
Combined mass of both cars = m1 + m2
Combined mass = 1000 kg + 100 kg
Combined mass = 1100 kg
Let the final velocity be v_final.
Step 4: Calculate the final velocity.
p_final = Combined mass × v_final
21109 kg·m/s = 1100 kg × v_final
v_final = 21109 kg·m/s ÷ 1100 kg
v_final ≈ 19.19 m/s
The negative sign indicates that the wreckage moves in the opposite direction to the initial velocity of the 1000-kg car. Therefore, the wreckage moves westward.
So, the wreckage moves westward with an initial speed of approximately 19.19 m/s.