An object with mass 3M is launched straight up. When it reaches its maximum height, a small explosion breaks the object into two pieces with masses M and 2M. The explosion provides an impulse to each object in the horizontal direction only. The heavier of the two pieces is observed to land a distance 53 m from the point of the original launch. How far from the original launch position does the lighter piece land

Explanation:

Each piece is analyzed by using the Principle of Momentum Conservation and the Impulse Theorem:

Heavier object:

Lighter object:

After the some algebraic handling, the following relationship is found:

Given that both pieces have horizontal velocities only and both are modelled as projectiles, the horizontal component of velocity remains constant and directly proportional to travelled distance. Then:

float.

archimedes' principle

denser than water sinks in water.

denser than mercury would sink in it