A bumper car with mass m1 = 106 kg is moving to the right with a velocity of v1 = 4.4 m/s. A second bumper car with mass m2 = 96 kg is moving to the left with a velocity of v2 = -3 m/s. The two cars have an elastic collision. Assume the surface is frictionless.What is the final velocity of car 1 in the ground (original) reference frame?
So far I have found velocity center of mass=.8831683168
initial velocity of car 1= 3.516831683
I have tried solving it by v2final=Vcm+V1 initial
where I got 4.4 but it's wrong
update: I got it, I just had to use v=-3.516831683+.8831683168
To find the final velocity of car 1 in the ground reference frame, you can use the conservation of momentum.
The momentum before the collision is given by:
p_initial = m1 * v1 + m2 * v2
Since the collision is elastic, the total momentum is conserved. The final velocity of car 1 can be found using the momentum after the collision:
p_final = m1 * v1_final + m2 * v2_final
Let's solve for v1_final:
Using the conservation of momentum, we have:
p_initial = p_final
Substituting the initial velocities and masses:
m1 * v1 + m2 * v2 = m1 * v1_final + m2 * v2_final
Now, rewrite the equation for v1_final:
v1_final = (m1 * v1 + m2 * v2 - m2 * v2_final) / m1
Substituting the given values:
v1_final = (106 kg * 4.4 m/s + 96 kg * (-3 m/s) - 96 kg * v2_final) / 106 kg
Now, you need to solve for v1_final by plugging in the value of v2_final.
To find the final velocity of car 1 in the ground reference frame after the elastic collision, we need to use the principle of conservation of momentum. This principle states that the total momentum before the collision is equal to the total momentum after the collision.
We can start by calculating the initial momentum of car 1, which is given by the product of its mass (m1) and velocity (v1):
Initial momentum of car 1 = m1 * v1 = 106 kg * 4.4 m/s = 465.6 kg m/s
Similarly, we can calculate the initial momentum of car 2:
Initial momentum of car 2 = m2 * v2 = 96 kg * (-3 m/s) = -288 kg m/s
Since the collision is elastic and there is no external force acting on the system, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we have:
Total momentum before collision = Total momentum after collision
Initial momentum of car 1 + Initial momentum of car 2 = Final momentum of car 1 + Final momentum of car 2
465.6 kg m/s + (-288 kg m/s) = m1 * Vfinal1 + m2 * Vfinal2
Now, since the final velocity of car 2 is given as -3 m/s (moving to the left), we can substitute the values and solve for the final velocity of car 1:
465.6 kg m/s + (-288 kg m/s) = 106 kg * Vfinal1 + 96 kg * (-3 m/s)
177.6 kg m/s = 106 kg * Vfinal1 - 288 kg m/s
177.6 kg m/s + 288 kg m/s = 106 kg * Vfinal1
465.6 kg m/s = 106 kg * Vfinal1
Vfinal1 = 465.6 kg m/s / 106 kg
Vfinal1 ≈ 4.39 m/s
Therefore, the final velocity of car 1 in the ground reference frame is approximately 4.39 m/s.