Question

two bodies are projected at angle theta and 90 minus theta to the horizontal with same speed find the ratio of their time of flights

Answer 1

Hi..

First of all you need to look at the sum of the given angle. θ+90-θ=90. Now they become complementary angles. I don't know if you know this but the projectiles having their θ as 90 have same range. So range ratio becomes 1:1

Time of flight is given by= 2usinθ/g (u being the initial velocity)
For 1 it becomes 2usinθ/g and for second- 2ucosθ/g (as sin(90-θ)=cosθ )
so ratio of time of flight is tanθ


Vertical height is given by u^2sin^θ/2g
for 1 it becomes u^2sin^θ/2g and for the second one it becomes u^2[sin(90-θ)]^2/2g
u^2cos^2θ/2g
so the ratio you will get is tan^2θ ....

Hope this helps u!!