Projectile Speed Comparison: Explaining with No Equations

[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.

 

[Tide]

HINT: Energy is conserved! :)

 

[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 v_A must equal v_B. Is this correct?

 

[Tide]

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