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Chapter 1: Q62P (page 97)

A rock is thrown with a velocity V0, at an angle of 伪0from the horizontal, from the roof of a building of height h. Ignore air resistance. Calculate the speed of the rock just before it strikes the ground, and show that this speed is independent of 伪0.

Short Answer

Expert verified

The speed v=v02+2ghis independent by 伪0.

Step by step solution

01

Introduction:

According to the law of conservation of energy, which is found in physics, the total energy of an isolated system is constant and is said to be conserved over time.

02

Consider the known data as below.

Angle is 伪0.

The mass of the rock is m.

Acceleration due to gravity is g.

Initial velocity is v0.

Final velocity of the rock is v.

Vertical distance from the ground is h.

03

Explanation:

The initial kinetic energy is,

KE1=12mv02

The initial potential energy is,

PE1=mgh

The final kinetic energy is,

KE2=12mv2

The final potential energy is,

PE2=0

Since the height is zero.

According to conservation of energy,

KE1+PE1=KE2+PE212mv02+mgh=12mv2+0v02+2gh=v2v=v02+2gh

And it can be seen that the velocity is independent of the angle 伪0.

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