Old cannons were built on wheeled carts, both to facilitate moving the cannon and to allow the cannon to recoil when fired. When a 150 kg cannon and cart recoils at 1.5 m/s, at what velocity would a 10 kg cannonball leave the cannon?

v2 = 22.5 m/s

Explanation:

Momentum is how hard to stop or turn a moving object. Generally, momentum measures mass in motion. Momentum is a vector quantity. Mathematically,

p = mass * velocity

The total momentum of an isolated system of bodies remains constant.

mometum before = 0

mass of the canon (m1) = 150 kg

mass of the ball (m2) = 10 kg

velocity of the ball (v2) = ?

velocity of the cannon (v1) = 1.5 m/s

momentum after = momentum before

m2v2 + m1v1 = 0

10v2 = 150 * 1.5

10v2 = 225

divide both sides by 10

v2 = 225/10

v2 = 22.5 m/s

22.5 m/s

Explanation:

Applying Newton's third law of motion

Momentum of the cannon and cart = momentum of the cannonball

MV = mv ... Equation 1

Where M = mass of the cannon and the cart, V = Recoil velocity of the cannon and the cart, m = mass of the cannonball, v = velocity of the cannonball

make v the subject of the equation

v = MV/m ... Equation 2

Given: M = 150 kg, V = 1.5 m/s, m = 10 kg

Substitute into equation 2

v = 150 (1.5) / 10

v = 22.5 m/s

Hence the cannonball leave the cannon with a velocity of 22.5 m/s