A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
Question
A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
Solution 1
Sure, I can help with that. Here's how you can solve this problem:
Step 1: First, we need to find the distance the girl has walked away from the lamp post after 4 seconds. Since speed = distance/time, we can calculate the distance as (1.2 m/s) * (4 s) = 4.8 m.
Step 2: Now, we have a right triangle where the lamp post is one side, the distance the girl has walked is the base, and the shadow is the hypotenuse. We can use similar triangles to find the length of the shadow.
The height of the lamp post is 3.6 m and the height of the girl is 0.9 m. The distance from the lamp post to the girl is 4.8 m. We can set up the following proportion:
(Height of lamp post / Height of girl) = (Distance from lamp post to girl / Length of shadow)
Step 3: Plugging in the known values, we get:
(3.6 m / 0.9 m) = (4.8 m / Length of shadow)
Step 4: Solving for the length of the shadow, we get:
Length of shadow = (4.8 m * 0.9 m) / 3.6 m = 1.2 m
So, the length of the girl's shadow after 4 seconds is 1.2 meters.
Solution 2
Sure, I can help with that. Here's how you can solve this problem:
Step 1: First, we need to find out how far the girl has walked away from the lamp post after 4 seconds. Since she is walking at a speed of 1.2 m/s, after 4 seconds she will have walked 1.2 m/s * 4 s = 4.8 meters.
Step 2: Now, we can use similar triangles to find the length of the shadow. The height of the lamp post and the height of the girl form two sides of two similar triangles, and the length of the shadow and the distance the girl has walked form the other two corresponding sides.
Step 3: So, we can set up the following proportion: (height of the girl / height of the lamp post) = (length of the shadow / (length of the shadow + distance the girl has walked))
Step 4: Plugging in the known values, we get (0.9 m / 3.6 m) = (length of the shadow / (length of the shadow + 4.8 m))
Step 5: Solving this equation for the length of the shadow, we get length of the shadow = 1.2 meters.
So, after 4 seconds, the length of the girl's shadow is 1.2 meters.
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