Physics 2D Momentum

Question

A 3520 kg truck moving north at 16.0 m/s makes an inelastic collision with a 1480 kg car moving 21.0 m/s east. What is the magnitude of their joint velocity after the collision?

Answer 1

First, I'd recommend drawing a diagram to get a fuller picture of what's happening. I'll try to approximate one here:

1480kg, 21.0m/s

[Car] ---> X

^

|

[Truck] 3520kg, 16.0m/s

Then find your equation for momentum and conservation of momentum.

p = mv

p_before = p_after = mv_before = mv_after = [car mv] + [truck mv] = [final mv]

Then, write down what you know. I'm going to call the car object 1 and the truck object 2.

m₁ = 1480kg

v₁=21.0m/s

m₂ = 3520kg

v₂ = 16.0m/s

We have enough information to find their momentum before the collision:

p₁ = m₁*v₁ = 1480kg * 21.0m/s = 31080 kg*m/s

p₂ = m₂*v₂ = 3520kg * 16.0m/s = 56320 kg*m/s

p_before = p₁ + p₂ = 31080 kg*m/s + 56320 kg*m/s = 87400 kg*m/s

Now, in this case, we have two bodies before the collision, and only one body after. The body will have its own separate speed, which is what we're solving for. Its mass is going to be both masses, added together.

m_f = m₁ + m₂ = 1480kg + 3520kg = 5000kg

So, assembling our final equation:

p_before = m_f * v_f

p_before/m_f = v_f

(87400kg*m/s)/(5000kg) = 17.48m/s

Unit check:

kg*m/s / kg = m/s

The correct unit for velocity, so our answer should be right!

The resulting speed of both vehicles combined is 17.48m/s.