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)

Accepted Answer

From $$\Delta ABD$$
$$	an 45 = {{{h_1}} \over d}$$
$$ \Rightarrow 1 = {{{h_1}} \over d} $$
$$\Rightarrow {h_1} = d$$
From $$\Delta ACE$$
$$	an 30 = {{{h_1} + {h_2}} \over {d + 2.464d}}$$
$$ \Rightarrow $$ $$0.5774 = {{d + {h_2}} \over {3.464d}}$$
$$ \Rightarrow $$ $$d + {h_2} = 0.5774 	imes 3.464 	imes d$$
$$ \Rightarrow $$ $${h_2} = 2.0001136d - d$$
$$ \Rightarrow $$ $${h_2} = 2.000d - d = d$$

Answer

0.464d

Answer

d

Answer

0.732d

Answer

1.464d

Motion in 2D & Vectors

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