Question

Consider two cases with different initial angles θ1 and θ2 and the same initial speed v0. What is the ratio of the times of the flights?

Answer 1

The formula for time for the highest point for projectile motion is

t =
`(V_(intial) * sin(theta) )/(g)`

This formula can be applied to the time for total distance( not just half to the highest point) because the time to reach the highest point is basically half of the total time. So even if you included the 2, it will be canceled out later because of the ratio.

t1 =
`(V_(intial) * sin(theta 1) )/(g)`

t2 =
`(V_(intial) * sin(theta 2) )/(g)`

We can cancel out the V intial and g because both equations have them

The differences are t1 = sin(theta 1) and t2 = sin (theta 2)

So to write it as a ratio

`(t_(1) )/(t_(2) ) = (sin (theta_(1)))/(sin(theta_(2)))`

This is answer. Good luck with projectile motion!