Question

How do you determine what velocity and angle is needed so that both the x and y displacement are equal to each other at a specific point?

For example if a projectile is launched on a 100m cliff, what velocity and angle is needed so that both the x and y displacement points are equal to 160m?

Answer 1

y-displacement is 160 m and height of cliff is 100m .so from origin (specific point) ,y-displacement is 160-100=60m and x-coordinate=160m .On equating their formulas ,we can get angle and velocity. I had taken your example as the situation and solve it for velocity and angle.You can generalise it for all cases.If there is no cliff then directly horizontal(x) and vertical displacement(y) can equate i.e no need to subtract height of cliff.