Question

While watching the clouds pass by, you notice a European swallow
flying horizontally at a height h = 21.4 m above you. When the swallow is directly
overhead, it drops an m= 11.1 kg coconut. From your ornithological studies, you know that
the air-speed of this particular species of swallow while carrying such a load is vo = 6.61
m/s. In this problem you may neglect air friction. Refer to the diagram. Assume the origin
of the coordinate system there is at your head.
Calculate the magnitude of the angular momentum of the coconut as observed by you one second after it is released

Answer 1

Answer:

magnitude of angular momentum of the coconut after t = 1 s is

$L = 1930.4 kg m^2/s$

Explanation:

Since it is dropped at the instant when it is at overhead position

so we will have

$v_x = 6.61 m/s$

now vertical speed of the coconut after t = 1 s

$v_y = 0 - gt$

$v_y = -9.8 m/s$

now its displacement in x direction is given as

$x = 6.61 (1) = 6.61 m$

height of the coconut after t = 1 s

$y = 21.4 - \frac{1}{2}gt^2$

$y = 21.4 - \frac{1}{2}(9.81)(1^2)$

$y = 16.5 m$

now angular momentum is given as

$L = \vec r \times m\vec v$

now we have

$L = (6.61 \hat i + 16.5 \hat j)\times (11.1)(6.61 \hat i - 9.81\hat j)$

$L = -719.8 \hat k - 1210.6\hat k$

so magnitude of angular momentum of the coconut after t = 1 s is

$L = 1930.4 kg m^2/s$

Answer 2

The magnitude of angular momentum of the coconut after t = 1 s is $L=1930.4kgm^2s^{-1}$

 Since it is dropped at the instant when it is at overhead position

∴ $v_x=6.61ms^{-1}$

Now vertical speed of the coconut after t = 1 s

$v_y=0+gt$

Displacement in x direction will be

x=6.61*1=6.61m

Height of the coconut after t=1s

$y=21.4-\frac{1}{2} gt^2\\\\y=21.4-\frac{1}{2}9.8(1^2)\\\\y=16.5 m$

∵Angular momentum is the rotational equivalent of linear momentum. Angular momentum is given as:

L= r × p

$L =(6.61{\boldsymbol {\hat {\imath }}}+16.5{\boldsymbol {\hat {\jmath }}})*11.1(6.61{\boldsymbol {\hat {\imath }}}-9.8{\boldsymbol {\hat {\jmath }}})\\L=-719.8 {\hat {k}}}-1210.6 {\hat {k}}}$

∴ magnitude of angular momentum of the coconut after t = 1 s is

$L=1930.4kgm^2s^{-1}$

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