the angle of projection of a body is 15 degree .the other angle for whioch the range is same as the firdt one is equal to?

Let a body is projected with speed u m/s at an angle α with horizontal ( or angle of projection is α).

then, horizontal range of the body, R = u²sin2α/g ......(1)

a/c to question,

range = distance covered by body in vertical direction in which body acquires velocity equals to velocity of projection.

i.e., R = h.....(2)

initial velocity of body along vertical direction = 0

final velocity , v = u

then using formula, v² = u² + 2as

or, u² = 0 + 2gh

or, h = u²/2g......(3)

from equations (1), (2) and (3),

u²sin2α/g = u²/2g

or, sin2α = 1/2 = sin30° or sin150°

or, 2α = 30° or 150°

or, α = 15° or 75°

hence, angle of projection : 15° or 75