Question

the max horizontal range of projectile is 400m then max height attained by it will be

Answer 1

by formula, of projectile motion .

Range = u²sin2∅/g

max height = u²sin²∅/2g

here u is the initial velocity of projectile , ∅ is angle of projectile with horizontal , g is acceleration due to gravity .

now, a/c to qn

R = 2H

u²sin2∅/g = 2u²sin²∅/2g

sin2∅ = sin²∅

2sin∅.cos∅ = sin²∅

2cos∅ = sin∅

tan∅ = 2

sin∅ = 2/√5

cos∅ = 1/√5

now,

Range = u²sin2∅/g

=u²{2sin∅.cos∅}/g

=u² {2 × 2/√5 × 1/√5 }/g

=4u²/5g