In 1780, in what is now referred to as \"brady\'s leap\", captain Sam Brady if t
ID: 1594930 • Letter: I
Question
In 1780, in what is now referred to as "brady's leap", captain Sam Brady if the US Continential Army escaped certain death by overing over the edge of the cliff above a river, which is confined at the spot to a gorge. He landed safely on the far side of the river. It was reported he leapt 22ft across while falling 20ft. Ignore aire resistance.
a) Representing the horizontal distance jumped as L and vertical drop as h, derive an expression for the minimum horizontal speed v(ax) he would need to make his leap if he ran straight (horizontally) off the cliff.
b) evaluate your expression for a 22ft jump with a 20ft drop to other side, giving the result in m/s.
c) Is it reasonable that a person could make this leap? Use the fact that the world record the 100m dash is approx. 10s to estimate the maximum speed such a runner would have.
Explanation / Answer
What is velocity that makes him go down 20 ' while pushing 22 feet?
First let us calculate the time required for any body for free fall of 20'
s=(1/2)gt^2
20=0.5*32*t^2
So, t =sqrt(40/32) = 1.118 second
In the same interval he has moved 22 feet horizontally(take component only)
Here, the horizontal velocity is unaffected by downward fall, of course neglecting air resistance.
S=time*velocity
velocity=22/1.118 = 19.67 feet/second
This is minimum velocity required to achieve that jump.
Explanation:
The idea is that these two motions act independently. By Newton's First law, the forward velocity is constant.
Vertical component component is again unaltered by horizontal motion component.