A 1093 kg van, stopped at a traffic light, is hit directly in the rear by a 715 kg car traveling with a velocity of +2.38 m/s. Assume that the transmission of the van is in neutral, the brakes are not being applied, and the collision is elastic. What is the final velocity of the car?
you get this one yet? can't figure it out either..
To find the final velocity of the car after the collision, we can use the principles of conservation of momentum and kinetic energy.
1. Conservation of momentum:
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
The initial momentum before the collision can be calculated as:
Initial momentum of the van (p_van_i) = m_van * v_van_i
Initial momentum of the car (p_car_i) = m_car * v_car_i
Since the van is at rest, its initial velocity (v_van_i) is zero (0). Therefore, the initial momentum of the van is zero.
So, the total initial momentum before the collision is only due to the car:
Initial total momentum (p_total_i) = p_car_i = m_car * v_car_i
2. Conservation of kinetic energy:
An elastic collision conserves kinetic energy, which means the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
The kinetic energy (KE) of an object is given by half the product of its mass and the square of its velocity: KE = (1/2) * m * v^2.
The initial kinetic energy before the collision can be calculated as:
Initial kinetic energy of the van (KE_van_i) = (1/2) * m_van * v_van_i^2
Initial kinetic energy of the car (KE_car_i) = (1/2) * m_car * v_car_i^2
Since the van is at rest, its initial kinetic energy (KE_van_i) is zero.
So, the total initial kinetic energy before the collision is only due to the car:
Initial total kinetic energy (KE_total_i) = KE_car_i = (1/2) * m_car * v_car_i^2
3. Using the principles of conservation of momentum and kinetic energy, we can calculate the final velocity of the car (v_car_f) after the collision.
After the collision, the momentum of the car and the total kinetic energy are conserved. Therefore:
Final momentum of the car (p_car_f) = p_total_i
Final kinetic energy of the car (KE_car_f) = KE_total_i
Using the equations for momentum and kinetic energy, we can find the relationship between the final velocity (v_car_f) and the initial velocity (v_car_i) of the car:
m_car * v_car_f = m_car * v_car_i (from conservation of momentum equation)
(1/2) * m_car * v_car_f^2 = (1/2) * m_car * v_car_i^2 (from conservation of kinetic energy equation)
Canceling the mass of the car (m_car) from both equations gives:
v_car_f = v_car_i
Therefore, the final velocity of the car after the collision is +2.38 m/s, which is the same as the initial velocity. In an elastic collision, when the object collides with a stationary object (in this case, the van), it retains its initial velocity.