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

Answer:

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

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

     $KE_i = \frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2$

substituting values  

    $KE_i = \frac{1}{2} * 30 * 3^2 + \frac{1}{2} * 35 * 1^2$

     $KE_i = 242.5 \ J$

The final kinetic energy of both skaters is mathematically represented as

       $KE_f = \frac{1}{2} * (m_1 + m_2 ) v_f^2$

substituting values

      $KE_f = \frac{1}{2} * (30 + 35 ) * 1.9^2$

      $KE_f = 117 \ J$

The lost in kinetic energy is

      $KE_l = 242.5 -117$

       $KE_l = 125.5 \ J$