Answer to Question #119968 in Mechanics | Relativity for Alex Kennedy

Question

A person standing on a bridge at a height of 115 m above a river drops a 0.250-kg rock. (a) What is the rock's mechanical energy at the time of release relative to the river surface? (b) What are the rock's kinetic, potential, and mechanical energies after it has fallen 75.0

Answer 1

Given data

Mass of rock is $m=0.250 kg$

Height is $y_0=115 m$

a)

The rock's mechanical energy at the time of release relative to the river surface is

$E=mgy_0=(0.250 kg)(9.80 m/s^2)(115 m)= 281.75 J$

b)

The rock's potential energy after it has fallen 75.0 m is

$U=mgy=(0.250 kg)(9.80 m/s^2)(40.0 m)=98 J$

The rock's kinetic energy after it has fallen 75.0 m is

$K=E-U=281.75 J-98 J=183.75 J$

The rock's mechanical energy after it has fallen 75.0 m is

$E=281.75 J$ Since law of conservation of energy.