A 114-g Frisbee is lodged on a tree branch 7.65 m above the ground. To free it, you lob a 240-g

step 1 Let us draw a diagram. This is the tree and this is ground and total height is 7 .65 meter from

A 114-g Frisbee is lodged on a tree branch 7.65 m above the...

A 114-g Frisbee is lodged on a tree branch $7.65 \mathrm{~m}$ above the ground. To free it, you lob a $240-\mathrm{g}$ dirt clod vertically upward. The dirt leaves your hand at a point $1.23 \mathrm{~m}$ above the ground, moving at $17.7 \mathrm{~m} / \mathrm{s}$. It sticks to the Frisbee. Find (a) the maximum height reached by the Frisbee-dirt combination and (b) the speed with which the combination hits the ground.

Key Concepts

Conservation of Momentum

This principle states that in the absence of external forces, the total momentum of a system remains constant during a collision or interaction. In scenarios involving collisions — including inelastic collisions where objects stick together — the final momentum of the combined system equals the sum of the momenta of the individual objects prior to the collision.

Inelastic Collision

An inelastic collision is a type of collision where the colliding bodies stick together after impact. Although kinetic energy is not conserved in such collisions, momentum is conserved. This concept is crucial when analyzing situations where two objects combine their masses and move together after collision.

Conservation of Energy

The conservation of energy principle states that energy can neither be created nor destroyed, only converted from one form to another. In mechanics, this often involves the transformation between kinetic energy and gravitational potential energy. When analyzing the movement of an object under gravity, energy conservation helps determine key quantities like maximum height reached or impact speed.

Projectile Motion

Projectile motion refers to the motion of objects launched into the air, subject to gravitational acceleration. In vertical projectile motion, the object’s kinetic energy converts to gravitational potential energy as it ascends, and vice versa as it descends. This concept provides the framework for analyzing the upward and downward trajectories of objects under gravity.

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