A Cadillac of mass 2210 kg going east collides with a Geo of mass 1240 kg headed north on a level highway. The cars remain tangled and slide to rest after traveling 25 m in a straight line at an angle of 20° north of east. The coefficient of kinetic friction for the tires on the road is 0.2. How fast was the Cadillac traveling before the unfortunate collision?
From the sliding distance and the coefficient of friction, compute the velocity of the joined pair immediately following the collsion.
MV^2/2 = mu*M*g*X
V^2 = 2*mu*g*X = 98 m/s
V = 9.90 m/s
Next, use conservation of momentum to solve for the initial speed of the Cadillac.
All of the eastward final momentum is due to the Cadillac's initial momentum.
3350 kg*9.90 m/s*cos 20 = 2210*Vcad,o
Solve for Vcad,o
A Toyota of mass 1500 kg is driving at 15 m/s NOrth when it rear-ends a Cadillac of mass 2500 kg also moving North at 9 m/s. (The driver of the toyota was probably texting) After the collision, the Toyota bounces back at 2 m/s. What is the speed of the Cadillac after the collision?
To find the initial velocity of the Cadillac, we can use the principle of conservation of momentum. The total initial momentum of the system is equal to the total final momentum of the system.
The momentum of an object is given by the product of its mass and velocity. Let's assume the initial velocity of the Cadillac is v1 m/s and the initial velocity of the Geo is v2 m/s.
The momentum of the Cadillac before the collision is given by:
Momentum1 = mass of Cadillac × velocity of Cadillac = 2210 kg × v1
The momentum of the Geo before the collision is given by:
Momentum2 = mass of Geo × velocity of Geo = 1240 kg × v2
The overall momentum of the system before the collision is equal to the vector sum of the momenta of both cars.
Now, let's break down the velocities into their respective components. The velocity of the Cadillac can be broken down into its east and north components, while the velocity of the Geo can be broken down into its east and north components as well.
The eastward component of the Cadillac's velocity is given by:
V1e = v1 × cos(20°)
The northward component of the Geo's velocity is given by:
V2n = v2 × sin(90°) = v2
The overall momentum in the eastward direction before the collision is given by:
Momentum1e = Momentum1 × cos(20°) = 2210 kg × v1 × cos(20°)
The overall momentum in the northward direction before the collision is given by:
Momentum2n = Momentum2 × sin(90°) = 1240 kg × v2
Since the collision causes the cars to come to rest, the final momentum in both the eastward and northward directions is zero.
The momentum in the eastward direction after the collision is given by:
Momentum1e + Momentum2e = 0
The momentum in the northward direction after the collision is given by:
Momentum1n + Momentum2n = 0
Now, we can substitute the component velocities into the momentum equations:
2210 kg × v1 × cos(20°) + 1240 kg × 0 = 0
2210 kg × 0 + 1240 kg × v2 = 0
Simplifying these equations, we get:
2210 kg × v1 × cos(20°) = 0
1240 kg × v2 = 0
Since the only way for the product of non-zero terms to be zero is if one of the terms is zero, we can deduce that v2 = 0. Therefore, the Geo was stationary before the collision.
Now we can solve for v1:
2210 kg × v1 × cos(20°) = 0
v1 × cos(20°) = 0
Since cos(20°) is non-zero, we can divide both sides of the equation by cos(20°) to isolate v1:
v1 = 0 / cos(20°)
v1 = 0 m/s
Therefore, the Cadillac was traveling at a speed of 0 m/s before the collision.