A subcompact car, mass 1,000 kg, runs into and sticks to an at rest, 2,200 kg SUV. If their final speed is 4.7m/s ,what was the smaller cars initial speed?
a) 67 m/s
b) 30m/s
c) 2.2 m/s
d) 15 m/s
final momentum = 4.7 (1000+2200)=15040
initial momentum = 1000 v
so
v = 15.04 m/s
15 m/s
To solve this problem, we can apply the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
The total momentum before the collision is the sum of the momenta of the subcompact car and the SUV. We can calculate the initial momentum of the subcompact car using the equation:
Initial momentum of subcompact car = Mass of subcompact car * Initial velocity of subcompact car
Let's assume the initial velocity of the subcompact car is v (unknown). So, the initial momentum of the subcompact car is 1000 kg * v kg/s.
The initial momentum of the SUV is zero because it is at rest.
Therefore, the total momentum before the collision is:
Total momentum before collision = initial momentum of subcompact car + initial momentum of SUV
= 1000 kg * v kg/s + 0 kg/s
= 1000v kg/s
After the collision:
The two vehicles stick together and move with a final velocity of 4.7 m/s. The total momentum after the collision is:
Total momentum after collision = Total mass * Final velocity
The total mass is the sum of the masses of the subcompact car and the SUV, which is 1000 kg + 2200 kg.
So, the total momentum after the collision is (1000 kg + 2200 kg) * 4.7 m/s.
According to the principle of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision:
1000v kg/s = (1000 kg + 2200 kg) * 4.7 m/s
Now we can solve this equation to find the initial velocity of the subcompact car (v).
v kg/s = (1000 kg + 2200 kg) * 4.7 m/s / 1000 kg
v kg/s = (3200 kg) * 4.7 m/s / 1000 kg
v kg/s = 15.04 m/s
Therefore, the initial velocity of the subcompact car is approximately 15.04 m/s.
So, the correct option would be:
d) 15 m/s