# Projectile Motion - Time in Air

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1. Nov 6, 2014

### air-in

1. The problem statement, all variables and given/known data
What angles should an arrow be launched if it leaves the bow @ speed of 60 m/s and is trying to hit a target that is 150 m away? Assume target is same height as bow.
Suppose the arrow is fired at an angle of 30 degrees & misses the target & hits the ground 1.8 m below from where it started. How much time was it in the air?

2. Relevant equations
1. t = 2vsinθ/g
2. t = √2y/g
3. Δy = (vsinθ)^2/2g

3. The attempt at a solution
I have attempted this the bold section of this problem a few different ways, but I am not convinced that any of them are correct. Could someone please tell me if any of them are correct, and if not, explain to me how to do it.

Attempt 1: t = 2(60)sin30/9.8
t = 6.1s

Attempt 2: t = √2(1.8)/9.8
t = .61s

Attempt 3: 1.8 = (vsin30)^2/2(9.8)
v = 8.4 m/s
t = 2(8.4)sin30/9.8
t = .86s

2. Nov 6, 2014

### _N3WTON_

Have you remembered to take into account the fact that the arrow lands 1.8m below it's original launch height?

3. Nov 6, 2014

### air-in

Wouldn't that be Δy, which I tried using in attempts 2 and 3?

4. Nov 6, 2014

### _N3WTON_

Now that you have edited your solution I believe that you are correct..