Question

Two bodies are projected at angle theta and 90 minus theta to the horizontal with the same speed the ratio of their maximum vertical height is?

Answer 1

the ratio of their maximum height = `(Tantheta )^2`

Explanation:

As the two bodies are being projected with velocity u
at angle `theta`

and `(90-theta`) respectively ,

their velocity component in vertical direction will be

`u. sin (theta)` and

`u .sin(90-theta) = u cos theta` respectively.

At the maximum height the final velocity (v) in vertical

direction will be zero for both bodies.

Therefore
using the relation between u, v and

the distance traversed h one can write -

`v^2 = u^2 - 2.g. h`

in which v=0 ; We get

`h = u^2/ (2g)` and

for first body height will be

`h1=( u.sintheta )^2 /(2g)`

and for the second body

`h2 =`(`u cos theta)`) ^2`/(2g)`

so `(h1)/ (h2 )= (Tan Theta)^2`