Question

A 30-kg skater moving at 3 m/s overtakes a 35-kg skater moving at 1 m/s in the same direction and collides with her. The two skaters stick together. It’s final speed is 1.9 m/s. How much kinetic energy is lost? Round all your answers to one decimal place.

Answer 1

The lost in kinetic energy is
`KE_l = 125.5 \ J`

Step-by-step explanation:

From the question we are told that

The mass of the first skater is
`m_1 = 30 \ kg`

The speed of the first skater is
`v_1 = 3 \ m/s`

The mass of the second skater is
`m_2 = 35 \ kg`

The speed of the second skater is
`v_2 = 1 \ m/ s`

The final speed of both skater are
`v_f = 1.9 m/s`

The initial kinetic energy of both skaters is mathematically represented as

`KE_i = (1)/(2)m_1 v_1^2 + (1)/(2)m_2 v_2^2`

substituting values

`KE_i = (1)/(2) * 30 * 3^2 + (1)/(2) * 35 * 1^2`

`KE_i = 242.5 \ J`

The final kinetic energy of both skaters is mathematically represented as

`KE_f = (1)/(2) * (m_1 + m_2 ) v_f^2`

substituting values

`KE_f = (1)/(2) * (30 + 35 ) * 1.9^2`

`KE_f = 117 \ J`

The lost in kinetic energy is

`KE_l = 242.5 -117`

`KE_l = 125.5 \ J`