Physics - Center of Mass Question with Solution | TestHub
A projectile of mass is fired so that the horizontal range is . At the highest point the projectile explodes in two parts of masses and respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is :
Options:
Answer:
Solution:
The initial horizontal velocity at the highest point is . The range is . At the highest point, the horizontal distance covered is .
The explosion is an internal force, so the center of mass continues its trajectory.
The heavier part () falls vertically, meaning its horizontal velocity is zero.
Let be the horizontal velocity of the lighter part ().
By conservation of momentum in the horizontal direction:
The lighter part travels for the same time as the original projectile would have taken to cover the remaining distance.
Distance covered by lighter part from explosion point: .
Total horizontal range of the lighter part = (distance to explosion point) + (distance after explosion)
Total range = .
The final answer is .