Will a falling monkey be hit by a bullet from 20 m away?

[luther_paul]

simple problem for you!

here's a simple homework problem!

a monkey is on a branch of a tree and a hunter aims with his rifle. at that moment when the hunter pulls the trigger, the monkey fell.
will the monkey be shot? assuming the height of the tree is 10 m.. and the hunter is 20m from the tree... assuming that the bullet travels off the barrel at standard velocity of a M16 assault rifle.

 

[himanshu121]

Equation of projectile is
$$y=x\tan{\theta}-\frac{gx^2}{2v_o^2cos^2\theta} ...A$$
So for x=20 and tan(theta)=10/20 similarly u can get value of cos(theta) and initial velocity given v₀

Also to travel x=20 bullet takes time t given by

$$v_0cos{\theta}t=20$$ ...1

In this time the monkey would have traveled
$$y=10-\frac{gt^2}{2}$$ .....2

from 1 & 2 & A

U can conclude that it would hit the (Poor)monkey

 

[HallsofIvy]

Actually there are a number of things left unsaid in this problem.

One, you must assume that we can neglect air resistance and friction.

Secondly we must assume that sights on the gun are not set to allow for bullet drop! Since the bullet drops (due to gravity of course), sights are normally set so that the barrel "aims" slightly above the target to allow for the drop over a given distance. Here we must assume that "aiming" at the monkey means that the bullet leaves the barrel along the straight line from the bullet to the monkey.

Assuming those things then the whole point of the question is that the downward acceleration of the bullet and monkey are exactly the same: -g. The fall of the bullet from a straight line will be exactly the same as the fall of the monkey and so the bullet will hit the monkey.

 

[Gara]

but the bulet isn't going in a straight line forward, the tree is 10 up, meaning he's aiming slightly upwards.

 

[HallsofIvy]

It doesn't matter that the straight line is not horizontal. The bullet's initial vertical velocity would take the bullet straight to the monkey, the monkey's initial velocity is 0. The vertical acceleleration of both monkey and bullet is the same.

(himanshu121's explanation is completely correct, just more than is necessary.)

 

[Raiden]

I think I had the same exact question on one of my physics test. I really hated that test. Anyway, what Himanshu said was right. At least, it was what my teacher told me was right.