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.

Question

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?

Answer 1

Vo = 14.5m/s @ 50 Deg.
Xo = 14.5cos50 = 9.32 m/s.
Yo = 14.5sin50 = 11.1 m/s.

a. Yf^2 = Yo^2 + 2g*h,
h = (Yf^2 - Yo^2) / 2g,
h = (0 - ( 11.1)^2) / -19.6 = 6.29 m.

b. V = Vf = 0 = Final Velocity.

c. d = Vo*t + 0.5g*t^2 = 6.29+10.
0 + 4.9t^2 = 16.29,
t^2 = 3.32,
t = Tf = 1.82 sw. = Fall time.

d. Vf^2 = Vo^2 + 2g*d,
Vf^2 = 0 + 19.6*16.29 = 319.28,
Vf = 17.9 m/s.

e. Tr = (Vf - Vo) / g,
Tr = (0 - 11.1) / -9.8 = 1.13 s. = Rise
time or time to reach max ht.

Tr + Tf = Time in flight.
Dx = Xo * (Tr+Tf),
Dx = 9.32 m/s * (1.13+1.82)s = 27.5 m.

Answer 2

post it.