Extreme-sports enthusiasts have been known to jump off the top of El Capitan, a

Question

Extreme-sports enthusiasts have been known to jump off the top of El Capitan, a sheer granite cliff of height 910m in Yosemite National Park. Assume a jumper runs horizontally off the top of El Capitan with speed 5.0m/s and enjoys a freefall until she is 150m above the valley floor, at which time she opens her parachute .
a)How long is the jumper in freefall? Ignore air resistance.
b)It is important to be as far away from the cliff as possible before opening the parachute. How far from the cliff is this jumper when she opens her chute?

Explanation / Answer

a)there was no initial vertical velocity, so we can calculate how long she was in free fall from

distance = 1/2 gt^2 where g is the accel due to gravity and t is the time

here, the distance of freefall = 910 m - 150 m = 760m

and find the time from

t=sqrt[2*760m/9.8m/s/s]=12.454 seconds

since there are no horizontal forces, the horizontal speed is constant throughout the trip (until the parachute is deployed)

therefore, the diver travels a horizontal distance of 5m/s x time of freefall

= 5*12.454=62.27m

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