ICA8 - This problem has three parts to this. I will state the questions for each of the three parts, along with any additional info below in "Description".

Question

Consider a truck, with mass 3000 kg, moving at 10 m/s in space relative to a nearby planet. The truck has a crate with a bed, which has a mass of 300 kg.

Part a) You devise a cannon that launches the crate out the back of the truck at a speed of 90 m/s, relative to the nearby planet. How fast is the truck going after launching the crate?

Part b) What is the magnitude and direction of the momentum of the truck with the crate and bed before the crate is launched?

Part c) What is the magnitude and direction of the momentum of the truck after the crate is launched?

Answer 1

This is a problem in conservation of momentum. The planet here is just a point of reference.

Part a) Suppose the initial direction of the truck is the "positive" direction and the opposite direction is the "negative" direction. Then, because of conservation of momentum, you have (Σm_i)v₀ = Σ(m_iv_fi) where the Σm_i is the total mass of the objects initially (this includes both the truck and the crate), and v₀ is the initial velocity of the truck with the crate; the right hand side is the sum of the momentums of each individual object (in this case, the truck and the crate). Try plugging in the values and see what you get.

Parts b) and c) This should follow directly from part a); the left hand side has the initial velocity of the truck with the crate, and one of the terms on the right hand side is the final momentum of the truck individually after the crate gets launched.