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

1 Answer
Feb 25, 2018

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