How Fast Must a Volcanic Bomb Travel to Reach a Certain Point?

[kara]

During volcanic eruptions, chunks of solid rock can be blasted out of the volcano; these projectiles are called volcanic bombs. At what initial speed would a bomb have to be ejected, at angle 35* to the horizontal, from the vent at A in order to fall at the foot of the volcano at B, at vertical distance h=3.30km and horizontal distance d=9.40km? Ignore, for the moment, the effects of air on the bomb's travel. What would be the time of flight? Would the effect of the air increase or decrease your earier answer?

Any suggestions for this question??

 

[Locrian]

Well, how are you setting up the problem? What equations do you think will be useful?

The only hint I can think to give without knowing how you are attacking the problem is this: these 2-d problems are often easier tackled if you think of them as two separate (but intimately related!) problems.

Break the initial velocity (even though it is unkown) into components. Now you have two problems: the first is this: how long to reach its peak and then fall to 3.30km above where it started? Knowing that you can solve the rest.

 

[nrobidoux]

I have the same homework problem... amazing how textbooks haven't changed a problem in a few years LOL.

I decided on using the equation y = x*tan(th)-g*x^2/(2*(v0*cos(th))^2)

Solving for v0, I got: v0 = (x/cos(th))*sqrt(g/(2*(x*tan(th)-y)))

Unfortunately the answer I got is completely different from the correct answer... well at least what the TA said was the correct answer. I'm getting something in the 400's m/2 ... without completely spoiling the answer for everyone he got something in the 200's.

For time I figure I'd solve, deltax = v0*cos(th)*t, for t... I just need to figure out how to get v0.

Thanks for any advice

(The radian equivalent of 35 degrees is 0.610865, yes?)

 

[nrobidoux]

Wow I figured it out... one of my usual mistakes. I used positive 3300 in my equations... not negative 3300