Jungle Veterinarian Shoots Monkey: Solving for Minimum Dart Velocity

[superdave]

A jungle veterinarian with a blow-gun loaded with a tranquilizer dart and a sly 1.5-kg monkey are each a height h above the ground in trees a distance L apart. Just as the hunter shoots horizontally at the monkey, the monkey drops from the tree in a vain attempt to escape being hit.

What must the minimum muzzle velocity of the dart have been for the hunter to hit the monkey before it reached the ground?

This should be just algebra, no numbers to input. But I can't get it right.

I first find the time for the monkey to hit the ground. Which is sqrt (2h/g).

Then I use L=vi*t+1/2at^2

From there I get vi=(L-1/2at^2)/t

Substituting for time I get (L-.5*2h)/sqrt (2h/g)

But that's not right.

 

[Galileo]

Then I use L=vi*t+1/2at^2

From there I get vi=(L-1/2at^2)/t

Why are you using L=vi*t+1/2at^2?
What is this 'a' in these equations supposed to represent?

 

[superdave]

Okay, yeah. That's wrong. I've been doing these problems for about 3 hours and my brain is fried. But then what do I use? does vf = 0?

 

[AKG]

How long does it take for a dropped object at initial height h to reach the ground?

v₁ = 0, a = -9.8, d = h, t = ?

The bullet has to travel a horizontal distance of L in that much time.

d = L, t = see above, v = ?

 

[Galileo]

Okay, yeah. That's wrong. I've been doing these problems for about 3 hours and my brain is fried. But then what do I use? does vf = 0?

You would use L=v_it+1/2at^2 if the bullet would be accelerating horizontally with a constant acceleration.
You have to treat the horizontal and vertical components of the bullet separately. Vertically it is accelerating due to gravity (same rate as the monkey), but what is the horizontal component doing?

EDIT: And ofcourse I meant tranquilizer darts. Shooting moneys with bullets is very badong.