A helicopter ascends and its height is given by y_plane = 3t^3 where h is in met

Question

A helicopter ascends and its height is given by y_plane = 3t^3 where h is in meters and t in seconds. At the time instance 2.0 s the helicopter releases a small mailbag. Use g 10 m/s2 and compute: The initial position and the initial velocity of the mailbag, when released from the helicopter. The maximum height the mailbag is going to reach. The time of flight of the mailbag from the instance it is released from the helicopter until it hits the ground. (in order to study the motion of the mailbag take t o the time instance the bag is released.) The velocity of the mailbag when it reaches the ground. Make a plot of u_y - t, y - t a_y - t for the mailbag (take t = 0 the instance the bag is released). it is given that the quadratic equation ax^2 + bx + c = 0 has solution given by:x = -b plusminus squareroot b^2 - 4ac/2a

Explanation / Answer

a)

yplane = 3 t3

at t = 2 , initial position is given as

Yo = initial Position = 3 (2)3 = 24 m

velocity at any time is given as

V(t) = dyplane /dt = 9 t2

initial velocity is given as

Vo = 9 (2)2 = 36 m/s

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