# ^Horizontal range

**^Horizontal range**

Horizontal distance in the plane of projection is called horizontal range, it is

Horizontal range is same for complementary angles.

The product of time of flights of two projectiles fired from same point with same speeds at complementary angles is

**Vertical range**

Diagram above shows a situation a projectile is fired at a speed u = 25 m/s. On changing the angle of projection its range and height changes. Note horizontal range is same for complimentary angles. Also vertical range is maxi if projection angle is maxi.

**Facts**

In going from O to A the following changes take place

- Change in speed = zero
- Change in velocity = 2u sinθ
- Change in momentum 2 mu sinθ
- in kinetic energy = zero
- Change in potential energy = zero
- Change in the direction of motion = ∠ 2θ

**Facts **

- Three particles A, B and C are thrown from the top of a tower with the same speed. A is thrown straight up, B is thrown straight down and C is thrown horizontally, then the speeds & time on hitting the ground are given as:

v_{A} = v_{B} = v_{C }and t_{A }> t_{C} > t_{B}

2. Suppose a body projected vertically upwards from the top of tower of height ‘h’ reaches the ground in t_{1} second. If it is projected vertically downwards from the same top with same velocity, it reaches the ground in t_{2} seconds. If it is just dropped from the top, it reaches the ground in t second, then