Quick Projectile Question

1. Dec 16, 2005

amcavoy

If two objects are fired, both from a height h and speed v0, where object A is fired at an angle θ with the horizontal and object B is fired at an angle of 2θ, which will land with a greater speed?

It seems to me that the speed would be the same for both, although the velocity vectors would differ in their x- and y-components. Is my answer correct? The question asks to explain this without any equations, so I am having trouble justifying it. Any ideas? Thank you.

2. Dec 16, 2005

Tide

HINT: Energy is conserved! :)

3. Dec 16, 2005

amcavoy

So if I use y=0 as my reference point and y=h as the launching point, I can say that:

Object A:

$$mgh+\frac{1}{2}m{v_{0}}^{2}=\frac{1}{2}m{v_{A}}^{2}$$

Object B:

$$mgh+\frac{1}{2}m{v_{0}}^{2}=\frac{1}{2}m{v_{B}}^{2}$$

Then vA must equal vB. Is this correct?

4. Dec 16, 2005

Tide

Yes, and you can even say that without using equations! :)