Free fall, hit the target, projectile problem

[annakwon]

Homework Statement

A monkey is free falling at a building at height 79.3 Meters. At the same time a dude shoots a dart from a building 65.2 meters tall, 81.0 meters away from monkey building, 55 m/s speed, angle at 10 degree.

Homework Equations

two dimension kinematics

The Attempt at a Solution

what i think...

1. In order for the dart to hit the monkey, they must intersect vertically directly under the monkey's starting position at some point above the ground.

2. Setting the vertical positions of the monkey and the dart equal to each other yields the following equation:

#1: v sin(θ)t - ½gt2 = h - ½gt2

which simplies to...

#2: v sin(θ)t = h

Then other thing i can use is... #3 v cos(θ)t = Distance of X

which will give me time.


I'm a bit confused from here. So the question needs "time" since i need to know what time the dart will hit the monkey (as monkey is falling down). I'm having hard time what i need to put in for the height. since its from building to building, not building to zero, do i subtract the two?

if my logic seems flawed, please help me

 

[Ibix]

The shooter is on top of another building - so your equation 1 is only correct if h is the difference between the heights of the buildings.

Fixing that, then #2 is an equation describing the vertical motion of the dart and monkey. Essentially, it tells you when the monkey drops below the dart.

On the other hand, #3 is talking about horizontal motion of the dart. It tells you when the dart passes the (vertically falling) monkey.

If the monkey drops past the dart at the same time as the dart passes the monkey, they hit.

This probably isn't right, because a dart doesn't follow a purely ballistic trajectory - it is also an aerodynamic body.

 

[annakwon]

Ok so, the question is if the dart will hit the monkey or not, so...55 sin (10) x t = H
55 sin (10) x t = 79.3 - 65.2
55 sin (10) x t = 14.1
t = 14.1/ 55sin10

t = 1.476

so if they were to hit, it should hit at 1.476

so...
v sin(θ)t - ½gt2 = h - ½gt2

55 (sin10) x 1.476 - (1/2)(9.8)(1.476^2) = 14.1 - (1/2)(9.8)(1.476^2)

is that right? if it equals it?

 

[Ibix]

Not quite. I agree with your calculation of t (at least as far as t=14.1/(55 sin(10)) - I haven't checked that you've put the numbers into the calculator correctly).

That tells you that the dart and the monkey are at the same height 1.476 after the monkey jumps and the man shoots. It doesn't tell you if they are at the same horizontal position or not.

How can you work out when they are at the same horizontal position?