A boy of height 95 cm is walking away from base of a lamp post at a speed of 1.5 m/s.If the lamp post is 3.8 m above the ground, find the length of his shadow after 5 seconds.

(x+7.5)/3.8=x/0.95

3.8x=0.95(x+7.5)
3.8x=0.95x+7.125
3.8x-0.95x=7.125
2.85x=7.125
285x/100=7125/1000
x=7125*2850
x=2.5

not a good solution

To find the length of the boy's shadow after 5 seconds, we need to determine how far the boy has moved away from the lamp post in that time.

First, let's convert the boy's height from centimeters to meters. Since 1 meter is equal to 100 centimeters, the boy's height in meters is 95 cm / 100 = 0.95 m.

Next, we can calculate the distance the boy has moved away from the lamp post by multiplying his speed (1.5 m/s) by the time (5 seconds):

Distance = Speed × Time = 1.5 m/s × 5 s = 7.5 m

Now, we can create a right triangle, where the height of the lamp post is the vertical side and the distance the boy has moved away from the lamp post is the horizontal side. The length of the boy's shadow is the hypotenuse of this triangle.

Using the Pythagorean theorem, we can calculate the length of the shadow:

Shadow Length = √(Distance^2 + Height^2)

Shadow Length = √(7.5^2 + 3.8^2)

Shadow Length = √(56.25 + 14.44)

Shadow Length = √70.69

Shadow Length ≈ 8.41 m

Therefore, the length of the boy's shadow after 5 seconds is approximately 8.41 meters.

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Nice solution

Assuming he started at the pole, after 5 seconds he is 7.5 m away.

So, if the shadow has length s, use similar triangles to get

(s+7.5)/3.8 = s/0.95

Now just solve for s.