Answer to Question #99557 in Mechanics | Relativity for Uchenna

Question

An arrow of Mass 0.3kg is fired with a velocity of 10m/s into a wooden block if mass 0.7kg.Calculate the final kinetic energy after impact, given that the wooden block can freely move

Answer 1

From the conservation of momentum:

$$mv=(m+M)u$$

$$(0.3)(10)=(0.3+0.7)u$$

$$u=3\frac{m}{s}$$

The final kinetic energy after impact:

$$K=0.5(m+M)u^2=0.5(0.3+0.7)3^2=4.5\ J$$