Name the principle on which ball pen works.
Answers
Explanation:
Let a \bold{\triangle}△ ABD having AB = height of tree and BC = x.
A man was standing on the bank of river and observes that angle of elevation of tree which is on the opposite bank of river is 60°.
When the man moves 50 m away from the bank i.e. CD the angle of elevation becomes 30° as shown in figure.
We have to calculate the height of the tree.
In \triangle△ ABC
\implies\:\dfrac{AB}{BC}\:=\:\tan\:\theta⟹
BC
AB
=tanθ
\implies\:\dfrac{h}{x}\:=\:\tan60^{\degree}⟹
x
h
=tan60
°
\implies\:\dfrac{h}{x}\:=\:\sqrt{3}⟹
x
h
=
3
\implies\:h\:=\:x\sqrt{3}⟹h=x
3
____ (eq 1)
Similarly,
In \triangle△ ABD
\implies\:\dfrac{AB}{BD}\:=\:\tan\:\theta⟹
BD
AB
=tanθ
\implies\:\dfrac{AB}{BC\:+\:CD}\:=\:\tan\:\theta⟹
BC+CD
AB
=tanθ
\implies\:\dfrac{h}{x\:+\:50}\:=\:\tan30^{\degree}⟹
x+50
h
=tan30
°
\implies\:\dfrac{h}{x\:+\:50}\:=\:\dfrac{1}{\sqrt{3}}⟹
x+50
h
=
3
1
\implies\:h\sqrt{3}\:=\:x\:+\:50⟹h
3
=x+50
\implies\:h\:=\:\dfrac{x\:+\:50}{\sqrt{3}}⟹h=
3
x+50
____ (eq 2)
From (eq 1) and (eq 2) we get,
\Rightarrow\:x\sqrt{3}\:=\:\dfrac{x\:+\:50}{\sqrt{3}}⇒x
3
=
3
x+50
\Rightarrow\:3x\:=\:x\:+\:50⇒3x=x+50
As, √3 × √3 = 3
\Rightarrow\:2x\:=\:50⇒2x=50
\Rightarrow\:x\:=\:25\:m⇒x=25m
Put value of x in (eq 1)
\implies\:h\:=\:25\sqrt{3}\:m⟹h=25
3
m
∴ Height of tree is 25√3 m.
Explanation:
The ball pen works on the principle of Capillary action and surface tension.