# Homework Help: Physics duck problem

1. Jul 27, 2010

### masohman

1. A duck flies horizontally with velocity v at a height h. When a duckhunter is right below it, he shoots with his shotgun. What is the minimum initial velocity V0 of the bullet and the angle a at which he shoots so that the bullet hits the duck?
Obviously, given are v, h and gravity acceleration g.

2.I think I just need to take that
Xduck = vt,
Xbullet = V0xt,
Ybullet = V0yt - 1/2 gt2,
Vy = V0y - gt for the bullet.

3.I just took
Xduck = Xbullet,
Yduck = Ybullet,
and Vy > 0 for the bullet
but I still get a result different than the one in my book.

2. Jul 27, 2010

### merryjman

All the things you have written are correct, assuming you are using h as the Y value for duck and bullet. Unless you use the Pythagorean Theorem for v0x and v0y then you're stuck with 2 equations and 3 unknowns (the 3rd unknown being the angle a).

3. Jul 28, 2010

### masohman

Yeah, I took Yduck = h.

My final result is that V0min = sqrt(v2 + 2gh) but the book says the answer is V0min = sqrt(v2 + 0.5gh)

4. Jul 28, 2010

### merryjman

Well, I don't know why your answer is different by that factor, but I do know that this is more easily solved using conservation of energy. Since it asks for the minimum speed, you can assume the bullet's vertical velocity is zero when it hits the duck, so it need only have enough kinetic energy to be moving at the same speed as the duck:

$$\frac{1}{2}$$mv02 = mgh + $$\frac{1}{2}$$mv2

and the correct answer for the speed comes pretty easily from that.

You can do the same thing with kinematics, I suppose, and make Vfy = 0