Question

Derive an expression for horizontal range of a projectile

Answer 1

Horizontal max distance travellef by a particle is called its range....

Here is its expression

R= horizontal speed × flight time

R= ucos theta × 2uSin theta /g

R= usq sin 2 theta /g

Answer 2

Projectile motion is a kind of motion in which an object is thrown into the air. Projectile motion has a curved path, and we can break this motion into a vertical component and a horizontal component.

The horizontal range of a projectile is the horizontal distance travelled by the projectile.

Let,

The object is projected with an angle of θ.

The time of the flight is T.

the component of the x axis is $u_{x} cos$θ.

The component of the y-axis is $u_{y} sin$θ.

We assume that the velocity does not change during the time of flight.

The y displacement becomes zero,

So,

0=$u_{y}$T-1/2g$T^{2}$

or, T=2$u_{y}$/g

or, T=2usinθ/g

So, the horizontal range will be R= 2$u^{2}$sin θcosθ/g

or, R= $u^{2} sin2$θ/g

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