posted by Aaron on .
A skydiver deploys his parachute when he is 950m directly above his desired landing spot. He then falls through the air at a steady 5.0 m/s . There is a breeze blowing to the west at 1.1 m/s.
At what angle with respect to vertical does he fall?
By what distance will he miss his desired landing spot?
a. Vo = 5m/s @ 270o + 1.1m/s @ 180o.
X = 5*cos270 + 1.1*cos180 = -1.1 m/s.
Y = 5*sin270 + 1.1*sin180 = -5 m/s.
tanAr = Y/X = -5/-1.1 = 4.54545
Ar = 77.6o = Reference angle.
A=180 + Ar = 180 + 77.6 = 257.6o, CCW.
A = 270 - 257.6 = 12.4o West of South.
b. Vo = -1.1/cos257.6=5.12 m/s @ 257.6o
Xo = 5.12*cos257.6 = -1.1 m/s.
Yo = 5.12*sin257.6 = -5.0 m/s.
h = Vo*t + 0.5g*t^2 = 950 m.
-5t + 4.9t^2 = 950
4.9t^2 - 5t -950 = 0
Use Quadratic formula:
Tf = 14.4 s. = Fall time.
Dx = Xo * Tf = -1.1m/s * 14.4=1.1 m.=
1.1m West of desired landing spot.
Yoe = 364(66)