Two vehicles with the same mass collide and lock together traveling 28 m/s at 37 degrees north of east after the collision. How fast was the car traveling that was heading north while the other vehicle was traveling east?

Perform a momentum balance.

Let V1 be the north-going car velocity, and V2, be the east-going car's velocity.

M V1 = 2M*28 sin 37
M V2 = 2M*28 cos 37

You can solve for both V1 and V2. The M's cancel.

To determine the speed of the car heading north, we need to calculate the velocity components of the vehicles before and after the collision. Let's break down the problem step-by-step:

Step 1: Identify the given information:
- After the collision, the vehicles travel together at a speed of 28 m/s.
- The direction of their motion is 37 degrees north of east.

Step 2: Determine the velocity components after the collision:
Since the vehicles move together after the collision, we can consider their velocities as a single vector. Using trigonometry, we can find the x and y components of the velocity vector.

The x-component (Vx):
Vx = V × cos(θ)
Vx = 28 m/s × cos(37°)
Vx = 22.258 m/s (rounding to three decimal places)

The y-component (Vy):
Vy = V × sin(θ)
Vy = 28 m/s × sin(37°)
Vy = 16.878 m/s (rounding to three decimal places)

Step 3: Analyze the problem:
Since the two vehicles had the same mass, we can assume that momentum was conserved during the collision. Therefore, the total momentum before the collision is equal to the total momentum after the collision.

Step 4: Determine the momentum before the collision:
Since we know the mass of the vehicles is the same, we can simplify the equation to:
p1 = p2

Let's assume the car heading north had a velocity of v m/s.

Momentum before the collision for the car heading north (∆p1):
∆p1 = mv1 = mv

Momentum before the collision for the car heading east (∆p2):
∆p2 = mv2 = m × 22.258 m/s (the x-component of the velocity after the collision)

Step 5: Set up the conservation of momentum equation:
∆p1 + ∆p2 = 0

mv + m × 22.258 m/s = 0

Step 6: Solve for the velocity of the northbound car (v):
mv = - m × 22.258 m/s
v = -22.258 m/s

The negative sign shows that the car heading north was traveling in the opposite direction after the collision. Therefore, the magnitude of its velocity is 22.258 m/s.

So, the car heading north was traveling at a speed of 22.258 m/s.