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?
Take free fall acceleration to be g.
cant find the answer for the life of me.
2007-10-24 06:15:18 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Physics
well since the dart falls at the same rate of the monkey the real question is how long does the monkey take to hit the ground. use the equation d=vot+1/2at²
refer to this website for further explination http://id.mind.net/~zona/mstm/physics/mechanics/kinematics/EquationsForAcceleratedMotion/EquationsForAcceleratedMotion.htm
d being h intitial velocity which you need to solve for (being the muzzle velocity) acceleration being g (9.81) t is the time in which it takes the monkey to fall to the ground.
hope that helps,
--mitsu
2007-10-24 06:26:27 · answer #1 · answered by n300zxtwin 2 · 0⤊ 0⤋
The time it takes for the monkey (and the dart) to hit the ground is:
t = sqrt(2H/g) from the equation x = 1/2at^2
Since both the dart and the monkey will be falling at the same rate, the dart must hit at or before the monkey hits the ground. therefore, the dart must be going at least at a velocity of:
v = L/t = L/sqrt(2H/g)
While the mass is not germane, it tells us that you are using MKS units so the above can be reduced using g=9.8.
v = 2.2L/√H
Any slower and the dart will hit the ground.
2007-10-24 06:25:03 · answer #2 · answered by gebobs 6 · 0⤊ 0⤋
Monkey And Hunter
2016-12-18 12:48:43 · answer #3 · answered by Anonymous · 0⤊ 0⤋
The dart will hit the monkey as long as it does not hit the ground first.
It was a height h above ground, so it will hit the ground in "square root of" h/4.9 seconds. [assuming h is in meters.]
It has to travel L meters in that time, so its minimum velocity must be:
L/t = L/(square root of h/4.9)).= L*Square root of (4.9/h)
2007-10-24 06:22:59 · answer #4 · answered by David Zukertort Rudel 3 · 0⤊ 0⤋
you don't have to worry about the monkey's mass in this problem.
we need to figure out vx of the gun.
first thing to do is figure out how long it takes the monkey to reach the ground
from s = s0 + v0*t + 1/2at^2 we can conclude
t = sqrt(2h/g)
the minimum vx = L/t = L/sqrt(2h/g)
2007-10-24 06:22:14 · answer #5 · answered by civil_av8r 7 · 0⤊ 0⤋
Are you planning on shooting a monkey anytime soon?
2007-10-24 06:18:57 · answer #6 · answered by JohnnyB 3 · 0⤊ 4⤋