# Horizontal Projectile

A body be projected horizontally from a certain height

*y*vertically above the ground with initial velocity*u*(Fig. 8). If friction is considered to be absent, the horizontal velocity remains constant.**Fig. 8**

# Trajectory of horizontal projectile

The horizontal displacement

*x*is governed by the equationThe vertical displacement

*y*is governed by(since initial vertical velocity is zero)

By substituting the value of

*t*in (5), .# Displacement of projectile

After time

*t*, horizontal displacement*x*=*ut*and vertical displacement .So, the position vector

**âˆ´â€‹**

and

# Instantaneous velocity

Throughout the motion, the horizontal component of the velocity is

*v*=_{x}*u*.The vertical component of velocity increases with time and is given by

*v*= 0 +

_{y}*gt*=

*gt*(From

*v*=

*u*+

*gt*)

So, =

i.e.,

Again

i.e.,

# Direction of instantaneous velocity

â‡’

where

*Ï†*is the angle of instantaneous velocity from the horizontal.# Time of flight

If a body is projected horizontally from a height

*h*with velocity*u*and time taken by the body to reach the ground is*T*, then# Horizontal range

Let

*R*is the horizontal distance traveled by a body, as shown in Fig. 9.**Fig. 9**

If projectiles

*A*and*B*are projected horizontally with different initial velocities from same height and third particle*C*is dropped from same point then- All three particles will take equal time to reach the ground.
- Their net velocity would be different but all three particles possess same vertical component of velocity.

**Fig. 10**

- They strike the ground with same speed at different times irrespective of their initial direction of velocities.
- Time would be least for particle
*E*which was thrown vertically downward. - Time would be maximum for particle
*A*which was thrown vertically upward.