Question

A projectile is launched vertically upward. It explodes into two pieces at the top point of its trajectory. One piece has twice the mass of the other. Immediately after the expIosion, the more massive piece has kinetic energy $E$. What is the total kinetic energy of both pieces immediately after the explosion?

• A. $1.5E$
• B. $2E$
• C. $3E$
• D. not enough information to answer
• E. Answer required

Answer 1

Answer: (C)

$3E$

$\text{Speed of heavier part (let's say 2m )}E=\frac{1}{2}\times 2m\times v^2\Rightarrow v=\sqrt{\frac{E}{m}}$

$\text{Speed of lighter part}=2v=2\sqrt{\frac{E}{m}}$

$\text{K.E. of lighter part}=E=\frac{1}{2}\times m\times 4\frac{E}{m}=2E$

$\text{Total K.E.}=3E$