Question

What is Horizontal range of the projectile ? Derive it’s formula.

Answer 1

The total distance covered by the projectile during it's time of flight is called horizontal range.

Formula for Horizontal range:

The horizontal distance travelled by the projectile is, x= uₓt

So, R = uₓ.T ( T = time of flight)

= ucosθ.(2usinθ/g)

= u².(2sinθcosθ/g)

= u²sin2θ/g

Thus, R = u²sin2θ/g

I hope this helps you.

Answer 2

Horizontal Range of Projectile:

• It is the horizontal component of displacement in a parabolic projectile trajectory.

• Let range be R :

• We know that time of projectile is : $T = 2u\sin(\theta)/g$

$\sf \: R = u_{x} \times T$

$\sf \implies R = u \cos( \theta) \times \dfrac{2u \sin( \theta) }{g}$

$\sf \implies R = \dfrac{2 {u}^{2} \sin( \theta) \cos( \theta) }{g}$

$\sf \implies R = \dfrac{ {u}^{2} \{2\sin( \theta) \cos( \theta) \} }{g}$

$\boxed{ \sf \implies R = \dfrac{ {u}^{2} \sin( 2\theta) }{g} }$

[Hence Derived]