Two cars approach along icy streets which meet at a right angle to one another. The cars collide and stick together. One car has a mass of 1200 kg and had a speed of 30 km/h in the +x direction before the collision. The second car has a mass of 1500 kg and was traveling in the +y direction before the collision. After the collision, the wreakage moved off at an angle of 64o to the x axis.
a) What was the initial speed of the heavier car?
b) What percentage KE was lost in the collision?
Help ASAP please!! Step by step to get the answers
What is it you do not understand here?
What equation to use and how to substitute it into the equation
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.
First, let's find the initial velocity of the heavier car (car 2).
a) To find the initial velocity of car 2, we need to find the velocity of the wreckage after the collision. We know that the wreckage moves off at an angle of 64 degrees to the x-axis.
Step 1: Decompose the velocity of the wreckage into its x and y components using trigonometry.
The x-component of the wreckage velocity (Vx) can be found using the equation: Vx = V * cos(θ), where V is the magnitude of the velocity and θ is the angle with the x-axis.
Vx = V * cos(64)
The y-component of the wreckage velocity (Vy) can be found using the equation: Vy = V * sin(θ).
Vy = V * sin(64)
Step 2: Apply the conservation of momentum in the x-direction.
Before the collision, car 1 is moving only in the x-direction, so its momentum in the x-direction is given by: P1x = m1 * V1x.
P1x = (1200 kg) * (30 km/h)
After the collision, the wreckage moves at an angle, so we need to consider its x-component of momentum (Px) only: Px = (m1 + m2) * Vx.
Px = (1200 kg + 1500 kg) * Vx
Since the momentum is conserved, P1x = Px.
Therefore,
m1 * V1x = (m1 + m2) * Vx.
Now we can plug in the values to solve for Vx:
(1200 kg) * (30 km/h) = (1200 kg + 1500 kg) * Vx.
b) To find the percentage of kinetic energy lost in the collision, we need to compare the kinetic energy before and after the collision.
Step 1: Calculate the initial kinetic energy of car 1 and car 2.
The initial kinetic energy of car 1 (KE1) is given by: KE1 = (1/2) * m1 * V1^2.
KE1 = (1/2) * (1200 kg) * (30 km/h)^2
The initial kinetic energy of car 2 (KE2) is given by: KE2 = (1/2) * m2 * V2^2.
Since car 2 is initially at rest, V2 = 0, so KE2 = 0.
Step 2: Calculate the kinetic energy of the wreckage after the collision.
The kinetic energy of the wreckage after the collision (KEw) is given by: KEw = (1/2) * (m1 + m2) * Vw^2.
We can find Vw by using the x and y components we calculated earlier:
Vw^2 = Vx^2 + Vy^2.
Finally, we can calculate the percentage of kinetic energy lost:
%KE lost = [(KE1 - KEw) / KE1] * 100.