A)Consider the setup of a gun aimed at a target (such as a monkey) as shown in t

Question

A)Consider the setup of a gun aimed at a target

(such as a monkey) as shown in the figure.

The target is to be dropped from the point A

at t = 0, the same moment as the gun is fired.

The bullet hits the target at a point P, which

is at the same horizontal level as the gun.

Let the initial speed of the bullet be v0,

let the angle between the vector ~v0 and the

horizontal (x-) direction be , and OP = L

and AP = h. The gravitational acceleration

is g. Denote the time taken to hit the target

by T.

The acceleration of gravity is 9.8 m/s2 .

B)Find the initial speed v0 (magnitude of the

vector ~v0) which allows the projectile to meet

the target at location P. (Hint: T defined in

part 1 is also the time taken for the bullet

to travel, following the projectile trajectory,

from O to P). Let the distance OP be L =

1.35 m, the angle = 42.4, and the time

T = 0.501573 s. (Given g = 9.8 m/s2).

= 3.64 m/s

C)Now the same setup is to take place at some

planet where the gravitational acceleration is

g' =g/4. Keep v0, and h to be the same as

before. Find the new height; i.e., the y-coordinate

of the new point of collision. (Hint: you

should convince yourself that for this new

case, the time taken for the bullet to travel

from O to the new point of collision P should

still be T).

I just need C answered.... #3/5/6 are ALL WRONG.

This time is given by T = y = 3 h/5 y = 2 h/3 y = h/2 y = h/3 y = h/4 y = h y = 3 h y = h/5 y = 3 h/4 y = 2 h

Explanation / Answer

since T will be same

sqrt(2*h/g) = sqrt(2*y/(g/4))

taking squares and solving

2*h/g = 8*y/g

y = h/4

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