a 2575 kg van runs into the back of a 825 kg compact car at rest. They move off together at 8.5 m/s. Assuming no friction with the ground, find the initial speed of the van.
To find the initial speed of the van, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v).
Given:
Mass of the van (m1) = 2575 kg
Mass of the compact car (m2) = 825 kg
Final velocity of both vehicles (Vf) = 8.5 m/s
Let's assume the initial velocity of the van (Vi1) is what we're trying to find, and the initial velocity of the car (Vi2) is 0 since it is at rest.
The total momentum before the collision is the sum of the individual momenta:
Total initial momentum = m1 * Vi1 + m2 * Vi2
= m1 * Vi1 + m2 * 0
= m1 * Vi1
The total momentum after the collision is:
Total final momentum = (m1 + m2) * Vf
According to the principle of conservation of momentum:
Total initial momentum = Total final momentum
m1 * Vi1 = (m1 + m2) * Vf
Now we can substitute the given values into the equation and solve for Vi1:
2575 kg * Vi1 = (2575 kg + 825 kg) * 8.5 m/s
Simplifying the equation:
2575 kg * Vi1 = 3400 kg * 8.5 m/s
Divide both sides of the equation by 2575 kg:
Vi1 = (3400 kg * 8.5 m/s) / 2575 kg
Vi1 ≈ 11.230 m/s
Therefore, the initial speed of the van is approximately 11.230 m/s.