Question

A projectile is fired at an angle with the horizontal with a small velocity. Its horizontal range will be maximum when the angle with the horizontal is

Answer 1

Horizontal range will always be maximum for angle with the horizontal as 45°

As Vertical velocity = Velocity × Sin of angle made with the horizontal

and Horizontal velocity =  Velocity × Cos of angle made with the horizontal

Time peroid = Time taken by the projectile to reach the ground = $\frac{2uSinΘ}{g}$

Where 'u' is the velocity of the projectile

           'Θ' is the angle made with the horizontal

Therefore Range = $\frac{u^{2} Sin( 2Θ) }{g}$

For the range to be maximum for a given velocity , Sin(2Θ) must be maximum.

Maximum value for Sin is 1 for an angle of 90°

Therefore ,

                               2Θ = 90°

                                 Θ = 45°