# Projectile motion of an arrow

1. Nov 14, 2006

### ornitho

im having a very difficult time with this question:

William Tell is said to have shot an apple off his son's head with an arrow. If the arrow was shot with an initial speed of 55m/s and the boy was 25m away, at what launch angle did William aim the arrow? The arrow and apple are initially at the same height above the ground.

2. Nov 14, 2006

$$x = v_{0}\cos \theta \; t$$
$$y = v_{0}\sin \theta\; t -\frac{1}{2}gt^{2}$$

$$v_{0} = 55$$

So you have:

$$25 = 55\cos \theta \; t$$
$$0 = 55\sin \theta\; t - 5t^{2}$$

Last edited: Nov 14, 2006
3. Nov 14, 2006

### ornitho

I do not have time value though :(

4. Nov 14, 2006

### ornitho

y = 0 wouldnt it, as it is returning to the initial y position, but i still do not understand how I am supposed to find t

5. Nov 14, 2006

The maximum altitude occurs at $$t = \frac{v_{0}\sin\theta}{g}$$.

The maximum altitude is: $$\frac{v_{0}^{2}}{2g}\sin^{2}\theta$$

6. Nov 14, 2006

### physics girl phd

That's right! now if you understand courtrigrad's earlier equations, for velocity and position, you have two equations, and two unknowns (t and the angle, theta). You can then solve the set of equations for both unknowns.

Last edited: Nov 14, 2006