How Long Does It Take for a Ball Launched Off a Cliff to Hit the Ground?

[TheDoorsOfMe]

Homework Statement

Ok, you have a cliff with height h and you launch a ball off of it at speed v and angle $$\theta$$. How long till it hit the ground?

Homework Equations

(1) Vsin($$\theta$$) = V$$_{y}$$
(2) V$$_{f}$$ = V$$_{y}$$ + at
(3) d = ((V$$_{i}$$ + V$$_{f}$$)/2)*t

The Attempt at a Solution

Ok, so what I did was take equation (2) and set V$$_{f}$$= 0. This alllows me to solve for the time that it takes to reach peak. Multiply this result by 2 to get the time when the ball is back to the plane of the cliff. Then for the time down to the ground I used equation (3) and plugged in V$$_{f}$$= $$\sqrt{V^{2}_{i}+2gh}$$ for V$$_{f}$$. Then I solved for t.

This lead to a result I feel looked to complicated for the question. Did I do this right?

Homework Statement

Homework Equations

The Attempt at a Solution

 

[TheDoorsOfMe]

Ok, I don't know why all my subscripts look like superscripts in this but they do. All those i's and f's are for intial and final velocity.

 

[kerimek]

Yes, your approach is correct. However, it may be helpful to simplify the equations by using the initial velocity in terms of its x and y components. This can be done by using equation (1) to find the initial velocity in the x direction (Vcos(\theta)) and then plugging that into equation (3). This will give you a simpler equation to solve for the time it takes for the ball to reach the ground. Also, make sure to keep track of the units and use appropriate units for each variable. Overall, your approach is correct and should lead you to the correct answer.