I believe I can Fly~I believe I can touch the sky

[maxtheminawes]

Homework Statement

Augustine continues to run around. He gets to the park and has the overwhelming urge to jump off a cliff and try to fly. He does so at an angle of 50 degrees to the horizontal while running at 14.5m/s. With his arms flapping, he rises in the air.
a) what is the highest point from the top of the cliff that he reaches before the laws of physics catch up with him and start bringing him back down to Earth?
b)What is his velocity at that point?
c)If the cliff is 10m high, how long is he in the air before he comes crashing down to the nice, soft, sandy beach below the cliff?
d)what is his final velocity?
e)what is his final horizontal displacement from the cliff?

Homework Equations

v=vo+at
y=yo+vot+1/2at^2
x=xo+vot+1/2at^2
v=final velocity
vo=initial velocity
yo=initial y displacement
xo=inital x displacement

The Attempt at a Solution

a) Vx=14.5cos50=9.32
Voy=14.5sin50= 11.11

v=vo+at
0=(9.32)+(-9.8)t
-9.32=-9.8t
-.95=t
.95sec=t

y=yo+vot+1/2at^2
y=11.11(.95)+1/2(-9.8)
y=1.23m


b)1.8m/s


c).95secs


d)v=vo+at
v=14.5+(-9.8)(.95)
v=5.59m/s


e)x=xo+vot+1/2at^2
x=14.5(.95)+1/2(-9.8)(.95^2)
x=23.85m

 

[ehild]

Distinguish between horizontal and vertical components of acceleration, velocity and displacement.
What is horizontal component of acceleration? ehild

 

[maxtheminawes]

i really have no clue. is it constant. i know that acc downwards is -9.8m/s^2

 

[HallsofIvy]

Yes, and (ignoring friction) that constant is 0! There is no horizontal force and so no horizontal component of acceleration.

 

[asteriatic]

I would like to remind you that the laws of physics do not allow humans to fly, no matter how strong our belief may be. What Augustine is experiencing is simply a result of his initial velocity and angle of jump, combined with the force of gravity. The highest point he reaches before falling back down is approximately 1.23 meters from the top of the cliff. At that point, his velocity is 1.8 m/s. If the cliff is 10 meters high, he will be in the air for approximately 0.95 seconds before landing on the beach below. His final velocity will be 5.59 m/s and his horizontal displacement from the cliff will be approximately 23.85 meters. These calculations are based on the assumption that there is no air resistance and that Augustine's body is a perfect projectile. In reality, air resistance and other factors would affect his trajectory and final outcomes. It is important to remember that while our imagination and beliefs can take us far, it is the laws of physics that ultimately govern our physical world.