Horizontal Range and Maximum Height of a Projectile

[darbeecakes]

Homework Statement

A ball is thrown vertically up from y=0 at time t=0 with v_initial=v₀j. Show that the time it takes for the ball to reach the ground is twice the time it takes to reach its maximum height.

Homework Equations

h=(v_i²sintheta_i)/2g
R=(v_i²sin2theta_i)/g

The Attempt at a Solution

I have no idea where to start solving this problem.

 

[Delphi51]

It is a purely vertical motion problem, so you can use just
V = Vo + at and d = Vo*t+½at²
Looks like you will have to get an expression for the time to maximum height and the time of the full flight back to ground.
It will be most helpful if you can see what the velocity is at maximum height and just before it hits the ground.

 

[darbeecakes]

I think I just have trouble figuring out what I need to solve for and what values to substitute where.

 

[Delphi51]

What is the velocity at the point of maximum height?
Substitute that into V = Vo + at and you will have the time of maximum height.

Do a very similar thing for the point where it hits the ground, and you'll have the full time of flight.