A moving object has a kinetic energy of 109 J and a momentum with magnitude of 40.0 kg·m/s. What is the mass and speed of the object?

Answer 1

Kinetic energy (E_K) is calculated as:

E_K = (1/2)mv² so

109 = (1/2)mv² or

218 = mv² (Equation1)

Momentum (P) is calculated as:

P = mv so

40.0 = mv which means m = 40/v

Plug in "40/v" in place of "m" in Equation 1

218 = (40/v)v²

218 = 40v

v = 218/40 = 5.45 m/s

Using m = 40/v, plug in v = 5.45 to get:

m = 40/5.45 = 7.34 kg

So the mass is 7.34 kg and the speed is 5.45 m/s