First slide

Projection from a balloon

Question

A helicopter is ascending vertically with a speed of 8.0 ms^-1. At a height of 12 m above the earth, a package is dropped from a window. How much time does it take for the package to reach the ground ?

Moderate

A

1.23s
B

3.23s
C

5.83s
D

2.53s

Solution

$t = \frac{{u + \sqrt {{u^2} + 2gh} }}{g}$
$I n i t i a l v e l o c i t y o f p a c k a g e = 8 m / s t i m e t a k e n t o r e a c h t h e h e i g h t 12 m a g a i n : 0.8 + 0.8 = 1.6 s e c v e l o c i t y a t h e i g h t 12 m = 8 m / s T h u s t i m e t a k e n t o r e a c h g r o u n d : v^{2} - u^{2} = 2 g \times 12 ∴ v^{2} = 240 + 64 v = \sqrt{304} v = 8 + g t t = 0.93 T h u s t o t a l t i m e = 1.6 + 0.93 = 2.53 s$

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