Question 108: Motion in 2D & Vectors

Question

A balloon is moving up in air vertically above a
point A on the ground. When it is at a height h
1
,
a girl standing at a distanced (point B) from A
(see figure) sees it at an angle 45
o
with respect
to the vertical. When the balloon climbs up a
further height h
2
, it is seen at an angle 60
o
with
respect to the vertical if the girl moves further
by a distance 2.464 d(point C). Then the height
h
2
is (given tan 30
o
= 0.5774)
![](https://imagex.cdn.examgoal.net/jgy2xukfga30if/452ea3e9-38ad-435d-8d50-b1a9c810b3ec/0c819d80-fe19-11ea-8293-3b6cc591631c/file-jgy2xukfga30ig-320w.png)

Accepted Answer

From $\Delta ABD$
$	an 45 = {{{h_1}} \over d}$
$ \Rightarrow 1 = {{{h_1}} \over d} $
$\Rightarrow {h_1} = d$
From $\Delta ACE$
$	an 30 = {{{h_1} + {h_2}} \over {d + 2.464d}}$
$ \Rightarrow $ $0.5774 = {{d + {h_2}} \over {3.464d}}$
$ \Rightarrow $ $d + {h_2} = 0.5774 	imes 3.464 	imes d$
$ \Rightarrow $ ${h_2} = 2.0001136d - d$
$ \Rightarrow $ ${h_2} = 2.000d - d = d$
![](https://imagex.cdn.examgoal.net/1kju91l5r/1f8c3c70-32be-4c2e-b201-0f5f0ad9c05d/d2510600-54f8-11eb-bb0e-bdf37f98ae86/file-1kju91l5s-421w.png)

Answer

0.464d

Answer

d

Answer

0.732d

Answer

1.464d

Motion in 2D & Vectors

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