a girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 metre if the length is 3.6 metre above the ground find the length of the shadow after 4 seconds
Answers
Correct question :-
A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 metre if the length is 3.6 metre above the ground find the length of her shadow after 4 seconds.
Solution :-
According to the given information draw a rough figure
[ Refer to attachment ]
Height of the lamp pole BC = 3.6 m
Height of the girl DE = 90 cm = 0.9 m [ Because 1 cm = 1/100 m ]
Speed of the girl = 1.2 m/s
Time taken to walk = 4 seconds
We know that
Speed = Distance / Time
⇒ Distance = Speed * Time
So, Distance walked by the girl from the lamp pole = 1.2 * 4 = 4.8 m = EB
Length of the shadow of the girl = AE
Consider ΔDEA and ΔCAB
DE ⊥ AB, CB ⊥ AB [ Heights are considered to be perpendicular to the ground ]
⇒ ∠DEA = ∠CBE = 90°
∠A is common
Third angles are also equal
Therefore by AAA similarity ΔDEA ~ ΔCAB
If 2 triangles are similar corresponding sides are in proportion
⇒ AE/AB = DE/CB
⇒ AE/(AE + EB) = DE/CB
⇒ AE/(AE + 4.8) = 0.9/3.6
⇒ AE/(AE + 4.8) = 9/36
⇒ AE/(AE + 4.8) = 1/4
⇒ 4AE = AE + 4.8
⇒ 4AE - AE = 4.8
⇒ 3AE = 4.8
⇒ AE = 1.6
Hence the length of the shadow of girl is 1.6 m.
