A helicopter carrying Dr. Evil takes off with a constant upward acceleration of

Question

A helicopter carrying Dr. Evil takes off with a constant upward acceleration of 7.0 m/s2 . Secret agent Austin Powers jumps on just as the helicopter lifts off the ground. After the two men struggle for 15.0 s , Powers shuts off the engine and steps out of the helicopter. Assume that the helicopter is in free fall after its engine is shut off, and ignore the effects of air resistance.

Powers deploys a jet pack strapped on his back 6.0 s after leaving the helicopter, and then he has a constant downward acceleration with magnitude 2.0 m/s2 . How far is Powers above the ground when the helicopter crashes into the ground?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Upward acceleration = 7m/s2

Time for which it accelerates = 15 seconds

height reached by helicopter = h=(1/2)*7*152 = 787.5 m

Height by which Powers and helicopter both fall during 6 seconds of free fall = (1/2)*9.8*62 = 176.4m

total time taken by helicopter to fall from highest point to ground = sqrt(2*787.5/9.8) = 12.68 seconds

after 1st 6 seconds, remqaining time taken by helicopter to fall to ground = 12.68-6=6.68 seconds

vecocity of Powers after fisrt 6 seconds = 9.8*6 = 58.8 m/s

acceleration of Powers after 6 seconds = 2m/s2

Distance travelled by Powers in remaining 6.68 seconds = (58.8*6.68)+(1/2)*2*6.682 = 437.41m

Total height by which Powers falls in when helicopter falls down to ground = 176.4+437.41 = 613.81m

height of Powers above ground when helicopter just falls on ground = 787.5-613.81 = 173.69m

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