Projectile motion of a bullet question

[Confused17]

Homework Statement

A hunter aims his gun at a monkey hanging from a high tree branch some distance away. At the instant the gun is shot the monkey drops from the branch, hoping to avoid the bullet. Assume there is no air resistance. Show analytically, using variables, that the monkey made the wrong move.

Homework Equations

d=V1t+1/2(a)t^2
Vvertical=V*sin(theta)

The Attempt at a Solution

dbullet=vbullet-4.9t^2
dmonkey=-4.9t^2

dmonkey=dbullet-vbullet

after this attempt I really have no idea what to do. I also subbed in made up values the speed and angle of the bullet to find vertical components but it was ineffective. Any help would be much appreciated.

 

[mgb_phys]

Calculate the height above the ground of the bullet with time, do the same for the monkey - if these are the same then that's probably bad news for the monkey.

 

[tomcue]

I would approach this problem by first defining the variables involved. We have the initial velocity of the bullet, vbullet, and the acceleration due to gravity, a. We also have the initial vertical velocity of the bullet, Vvertical, which can be found using the formula Vvertical = V * sin(theta), where theta is the angle at which the gun is aimed.

Next, we can use the equation for the vertical displacement of an object under constant acceleration, d = Vt + 1/2at^2, to determine the vertical distance traveled by both the bullet and the monkey.

For the bullet, the vertical distance traveled can be written as dbullet = Vvertical * t + 1/2 * a * t^2.

For the monkey, since it is initially at rest, the vertical distance traveled can be written as dmonkey = 1/2 * a * t^2.

Now, if we assume that the monkey dropped from the branch at the same time the bullet was fired, we can set these two equations equal to each other and solve for t.

Vvertical * t + 1/2 * a * t^2 = 1/2 * a * t^2

Solving for t, we get t = 0, meaning that the monkey and the bullet will reach the same vertical position at the same time. This means that the monkey cannot avoid the bullet by dropping from the branch, as it will still be in the bullet's path.

In conclusion, analytically, we can show that the monkey made the wrong move by using the equations for projectile motion and assuming that the monkey dropped from the branch at the same time the bullet was fired. This analysis assumes no air resistance, and in reality, the outcome may be slightly different due to factors such as air resistance and the initial velocity of the monkey.