Question

find the angle of projection for which range and maximum height will be equal.

Answer 1

we know,
Range = u²sin2∅/g
and maximum height = u²sin²∅/2g

where , u is initial velocity , ∅ is the angle of intial velctiy with horizontal . and g is acceleration due to gravity .

now, A/C to question .

Range = maximum height
u²sin2∅/g = u²sin²∅/2g
sin2∅= sin²∅/2

we know, sin2∅ = 2sin∅.cos∅ use , this
2sin∅.cos∅ = sin²∅/2
cos∅ = sin∅/4
tan∅ = 4
∅ = tan^-1( 4)

hence, angle of projection = tan^-1(4)