Question

What is projectile?show that its path is parabolic and derive expression for maximum height, time of flight and horizontal range.

Answer 1

Projectile motion is a form of motion experienced by an object or particle that is thrown near the Earth's surface and moves along a curved path under the action of gravity only. This curved path was shown by Galileo to be a parabola. 

Answer 2

Definition :the motion of a particle due to a initial velocity which was given to it initially without any propulsion

Derivation :

Initial velocity u and with angle ¤

The velocity of projectile is u which makes¤ with horizontal

Vertical component of the initial velocity uy = usin¤

Horizontal component of the initial velocity ux = ucos ¤

Let , T be the time of flight .so the max height is reached at T/2

The vertical component became 0 at the maximum height H

Using

V = u+at

0 =uy -gt 0 = uy -gt

t= usin¤/g=T/2

T= 2usin¤/g

For height

S= ut+1/2at^2

H=uyT/2-1/2g(T/2)^2

H= usin¤*usin¤/g-1/2g*u^2sin^2¤/g^2

H=u^2sin^2¤/2g

For range

R=yxT

R=ucos¤*2usin¤/g

R=u^2sin2¤/g