1)A 1180-kg van, stopped at a traffic light, is hit directly in the rear by a 753-kg car traveling with a velocity of +1.81 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 (a) the car and (b) the van?
I was going to use the equation
m1v1 + m2v2 / m1+m2 but then i realized that I have to find the velocity for both of the cars and now I am confused.
To find the final velocities of both the car and the van after the collision, you can use the principles of conservation of momentum and kinetic energy.
Let's break down the problem step by step:
Step 1: Find the initial momentum of each object.
The initial momentum of an object is the product of its mass and velocity. The momentum is given by the equation: p = m * v.
For the van:
Initial momentum of the van = mass of the van * initial velocity of the van
p1 (van) = m1 (van) * v1 (van) = 1180 kg * 0 m/s (since the van is stopped)
For the car:
Initial momentum of the car = mass of the car * initial velocity of the car
p1 (car) = m2 (car) * v1 (car) = 753 kg * 1.81 m/s
Step 2: Apply conservation of momentum.
According to the law of conservation of momentum in an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the sum of the initial momenta of the car and the van is equal to the sum of their final momenta.
p1 (van) + p1 (car) = p2 (van) + p2 (car)
Step 3: Simplify the equation.
Substitute the initial and final velocities of the van and the car into the conservation of momentum equation:
m1 (van) * v1 (van) + m2 (car) * v1 (car) = m1 (van) * v2 (van) + m2 (car) * v2 (car)
Step 4: Solve for the final velocities.
Using the equation found in step 3, you can isolate the final velocities of the van and the car:
v2 (van) = (m1 (van) * v1 (van) + m2 (car) * v1 (car) - m2 (car) * v2 (car)) / m1 (van)
v2 (car) = (m1 (van) * v1 (van) + m2 (car) * v1 (car) - m1 (van) * v2 (van)) / m2 (car)
Substituting the known values into these equations will give you the final velocities of the van and the car.
Note: Since this is an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. If you want to calculate the kinetic energy of each object after the collision, you can apply the same principles.