Question

Show that the maximum horrizontal range of a projectile is four times the corresponding maximum height?

Answer 1

Range of a projectile is given by the formula, `R= (u^2 sin 2theta)/g` (where, the projectile was projected with initial velocity `u` at angle `theta` w.r.t horizontal)

And, maximum height reached by projectile is expressed as `H= (u^2 sin ^2 theta)/(2g)`

Now, `R` will be maximum when, `sin 2 theta` is maximum,so maximum value of `sin 2theta` is `1`, so `2theta=90` or, `theta =45`

So, now `R= u^2/g`

And, `H= (u^2 sin^2 45)/(2g) = u^2/(4g)=R/4`

so, `R=4H`