Collision

[NA19]

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Two guns, separated by five meters and pointed at each
other, are tilted so that each gun points at an angle  above
the horizontal. Both guns are fired simultaneously, with
each bullet leaving its gun at a speed of 250 m/s. The bullets
collide inelastically in midair, falling together to the
ground.

How much time elapses between the firing
of the guns and the collision of the two bullets?

I tried to use the equation vy = v0y - gt
So I got 25sintheta = t

However, the answer is apparently 0.01/costheta.

If someone could explain, that would be great!

 

[FeinMS]

They're 5 meters apart, shoots at the same velocity. The bullet will collide at the midpoint. (2.5 meters away from each gun) You can say that the horizontal displacement is 2.5 meter, and x=V0*cos(theta)t. This gives t=x/(V0*cos(theta))=2.5/(250*cos(theta))=0.01/cos(theta)

 

[NA19]

Why can't you use the vy equation?

 

[FeinMS]

Why can't you use the vy equation?

Not very useful because dy of both bullet is the same at every point while dx only equal when they're at the midpoint which is the point of interest

 

[NA19]

Not dy, vy = v0y - gt. Why is 25 sintheta wrong?

 

[FeinMS]

Not dy, vy = v0y - gt. Why is 25 sintheta wrong?

I tried to use the equation vy = v0y - gt
So I got 25sintheta = t

First you're using an approach that doesn't make sense. To find the time at which they collide, you can't use vy. Vy is always the same for both bullets. The only way to find the point of collision in this case is by setting Dx of one bullet=Dx of another.

Second your algebra is wrong. Vy=V0y - gt. V0y is definitely 250 sin(theta), but you obviously ignored Vy and simply set V0y/g=t

 

[monkeyvokes]

yeah you want the horizontal velocity, V*cos theta
then, since v = meters / time, you can do meters divided by the horizontal velocity
2.5/ 250 cos theta
0.01 / cos theta

 

[NA19]

Isn't vy zero at the collision point because it's the top of the parabola?

 

[monkeyvokes]

Seems like this scenario could result in vy=0 upon collision if given the proper value for theta, but doesn't have to