A small sphere of mass m is launched horizontally over a body of water from a height h above the water and with a launch speed v0. Determine expressions for the following in terms of m, v0, h, and g. Air resistance is negligibly small.

(a) W is the amount work done by the force of gravity on the projectile during its flight.
(b) ΔKE is the change in kinetic energy ΔKE of the projectile from the time it was fired until it hits the water.
(c) KEf is the final kinetic energy KEf of the projectile as it hits the water.

(a)

F=mgh

(b)

(c)

Explanation:

(a)

Work done by gravity is given as the product of force and perpendicular distance hence

W=Fh

Where F is force and h is perpendicular height.

Since force due to gravity is a product of mass and acceleration due to gravity, ie F=gm then substituting this back into the original formula, we obtain

F=mgh

(b)

Kinetic energy, KE is given by

where m is the mass of an object and v is the velocity. Taking final velocitu as vf while initial velocity as given vo then change in kinetic energy is given by the difference between final and initial kinetic energy

Intial kinetic energy is

Final kinetic energy is

Change in kinetic energy is given as

(c)

As already derived in part b above, the final kinetic energy is equivalent to Final kinetic energy is

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.