A girl of height 1.2 m is walking away from the base of lamp post at the speed 1.5m/sec .if the bulb is at 4.5m height from the ground find lenght of the shadow of the girl after 5 sec
Answers
Answer:
2.14 m
Step-by-step explanation:
Let AB be the lamp post.
CD be the girl and D be the position of the girl after 4 seconds.
Again, let DE = x metre be the length of the shadow of the girl.
Given,
CD= 1.2 m, ie, 120cm
AB= 4.5m
Speed of girl = 1.5m/s
Using the formula "Distance = Speed x Time"
We find the distance of the girl from the lamp post after 4 seconds.
A/Q,
BD= 1.5×5
BD= 7.5 m
Then we show that △ABE∼ΔCDE
In △ABE and △CDE, we have,
Angle B= Angle D [Each90∘]
Angle E= Angle E [ Common Angle ]
∴△ABE∼ΔCDE[ By AA Similarity Criterion]
∴BE/DE=AB/CD…… (i)
Now substituting all the values in equation (1), we get
7.5+x divided by x=4.5/1[∵BE=BD+DE=7.5+x]
=>7.5+x/x = 4.5
=>7.5+x = 4.5x
=>3.5x = 7.5
⇒>x = 7.5/3.5
⇒x = 2.14 metre
Hence, the length of shadow after 5 seconds is 2.14 m.
Thank you for asking this question. Here is your answer:
Height of the girl is 1.2 m
Height of the lamp is 3.6 m
We will let x be the shadow length
Distance traveled in 4 second = 0.6 x 4 = 2.4 m
From the properties of similar triangle;
1.2/3.6 = x /( x + 2.4)
3x = x + 2.4
2x = 2.4
x = 1.2 m
Length of the shadow will be 1.2 m
If there is any confusion please leave a comment below.