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 in the bed, which has a mass of 300 kg.

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?

Answer 1

The speed of the truck after launching the crate is -3 m/s.

Step-by-step explanation:

The speed of the truck after launching the crate can be determined using the principle of conservation of momentum. The momentum before launching the crate is equal to the momentum after launching the crate.

Before launching the crate:

• The mass of the truck (m1) = 3000 kg
• The velocity of the truck (v1) = 10 m/s

The momentum before launching the crate (p1) = m1 * v1

After launching the crate:

• The mass of the truck (m1) = 3000 kg
• The velocity of the truck after launching the crate (v2)
• The mass of the crate (m2) = 300 kg
• The velocity of the crate relative to the planet (v3) = 90 m/s

The momentum after launching the crate (p2) = (m1 * v2) + (m2 * v3)

Since momentum is conserved, we can set p1 equal to p2:

m1 * v1 = (m1 * v2) + (m2 * v3)

Solving for v2 (the velocity of the truck after launching the crate):

v2 = (m1 * v1 - m2 * v3) / m1

Substituting the given values:

v2 = (3000 kg * 10 m/s - 300 kg * 90 m/s) / 3000 kg = -3 m/s

The speed of the truck after launching the crate is -3 m/s.