Question

Why do projectiles with angle 45 make the biggest range?

why do projectiles with angle 45 make the biggest range?

Answer 1

If a projectile is thrown with a velocity `u` with an angle of projection `theta`,its range is given by the formula, `R=(u^2 sin 2theta)/g`

Now,if `u` and `g` are fixed, `R prop sin 2 theta`

So,`R` will be maximum when `sin 2 theta` will be maximum.

Now,maximum value of `sin 2theta` is `1`

if, `sin 2theta=1`

so,`sin 2theta =sin 90`

so,`2 theta=90`

or, `theta=45^@`

That means,when angle of projection is `45^@` range is the maximum.