dart with a mass of 50 g is thrown at 15 m/s and sticks into a 100-g apple hanging on a string. What is the velocity of the dart and apple just after the dart is embedded

5 m/s

Explanation:

From the law of conservation of momentum,

mu+m'u' = V (m+m') ... Equation 1

Where m = mass of the dart, m' = mass of the apple, u = initial velocity of the dart, u' = initial velocity of the apple, V = the velocity of the dart and the apple after after they are embedded.

Making V the subject of the equation,

V = (mu+m'u') / (m+m') ... Equation 2

Given: m = 50 g = 0.05 kg, m' = 100 g = 0.1 kg, u = 15 m/s, u' = 0 m/s (at rest)

Substitute into equation 2

V = (0.05*15+0.1*0) / (0.05+0.1)

V = 0.75/0.15

V = 5 m/s.

Hence the velocity of the dart and apple = 5 m/s