Physics: Un paracaidista salta desde una altura de 3 km. Tras caer libremente durante 50m, abre su paracaídas y desde ese momento cae a una velocidad constante. ¿Cuánto ha durado su caída libre?

Un paracaidista salta desde una altura de 3 km. Tras

mads000

29.06.2020

97.44 s

Explanation:

During the first 50 meters, the motion of the skydiver is a free-fall motion, so it is a uniformly accelerated motion with constant acceleration

g=9.8 m/s^2

downward.

Therefore, the time taken to covere these first 50 meters is given by

$s=ut+\frac{1}{2}gt^2$

where

s = 50 m is the displacement

u = 0 is the initial velocity

g=9.8 m/s^2 is the acceleration

Solving for t,

$t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(50)}{9.8}}=3.19 s$

After this first phase, the velocity of the skydiver is:

v=u+gt=0+(9.8)(3.19)=31.3 m/s

After this point, the skydiver continues his motion at constant speed, so the time taken to cover the second part is

$t'=\frac{d}{v}$

where:

d = 3000 m - 50 m = 2950 m is the distance left

v = 31.3 m/s is the speed

So,

$t'=\frac{2950}{31.3}=94.25 s$

So, the total time of flight is

T=t+t'=3.19+94.25=97.44 s

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