In lecture we saw the “Shoot the Monkey” demo. In short a spring-loaded gun is p

Question

In lecture we saw the “Shoot the Monkey” demo. In short a spring-loaded gun is placed on a platform and aimed at a monkey a horizontal distance D away and a vertical distance h off the ground (see figure). Assuming the monkey doesn’t hit the ground first, you will show (by solving the below questions) that it will always get hit. Note: you will need to define some parameters that aren’t given in the drawing to solve this problem.

a.) What is the time it takes the bullet to go a horizontal distance D.

b.) What is the height of the bullet at that time? What is the height of the monkey at that time? Are they the same?

Explanation / Answer

a) time taken by bullet to travel D distance in horizontal.

t = D / v cos@

where cos@ = D / sqrt(D^2 + h^2)

t = sqrt(D^2 + h^2) / v

b) In vertical,
For Bullet,

y = vsin@*t - gt^2 /2

y = v(h / sqrt(h^2 + D^2))(sqrt(D^2 + h^2) / v) - g(sqrt(D^2 + h^2) / v)^2 /2

yb = h - g(D^2 + h^2)/2v^2

Height of monkey that time,

In time it will drop y =0 - gt^2 /2 = gt^2 /2

and initially it was at h height.

so from ground y = h - gt^2 /2

ym = h - g(sqrt(D^2 + h^2) / v)^2 /2   

ym = h - g(D^2 + h^2)/2v^2

so ym = yb are same.

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