# 2) You are working as a student intern for the National Aeronautics and Space Administration (NASA) and your supervisor wants you to perform an indirect calculation of the upward velocity of the Space Shuttle relative to the Earth’s surface just 6.1 seconds after it is launched when it has an altitude of 100 meters. In order to obtain data, one of the engineers has wired a streamlined flare to the side of the shuttle that is gently released by remote control after 6.1 seconds. If the flare hits the ground 8.5 seconds after it is released, what is the upward velocity of the flare (and hence of the Shuttle) at the time of its release? (Neglect any effects of air resistance on the flare.) Note: The flare idea is fictional but the data on a typical Shuttle altitude and velocity at 6.1 seconds are straight from NASA!

The initial speed of the flare on the vertical axis `V_(0y)` is equal the the upward speed of the shuttle. The flare is released from an initial height of `H =100 m` m and its motion is uniform accelerated with the acceleration `-g` downwards (because of the flare form the resistance of the air can be neglected). For the uniform accelerated motion, the relation between space, initial speed and acceleration is

`H = V_(0y)*t - (g*t^2)/2`

`V_(0y)*t = H+(g*t^2)/2`

`V_(0y) = H/t +(g*t)/2 =100/8.5 +9.81*8.5/2 =53.46 m/s`

The upward velocity of the flare (Shuttle) at the time of its release is 53.46 m/s.

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