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The shadow cast by a man standing 1 m from lamp post is 1.2m long. If the man is 1.8 m tall and wals away from the lampost at a speed of 120m/min, at what rate is the shadow lengthening after 5 s?

The height of the light is 3.5 and the height of the man is 1.8.

The distance to the man is 1 meter at the start and the length of the shadow is 1.2 meters.

This means that the length of the shadow is 1.2 times longer

than the difference between the man and the pole.

After 5 seconds, the man has traveled for 1/12 of a minutes.

This means he is 120/12 = 10 meters farther away.

Since he started 1 meter away from the pole, he is now 11 meters away from the pole.

Since the ratio of the distance is 1.2 to 1, this means we have to take 11 * 1.2 = 13.2 meters.

Since the man is 1.8 meters tall, (13.2/1.8)120m/min is how fast the shadow is moving at.

Now 13.2/1.8 x 5/5 = 66/9 = 22/3, so the shadow is growing at 22/3 the speed he is walking.

Since he is moving at 120m/min, the length of the shadow is increasing at

120(22/3) = 40*22 = 880 m/min.

Calculus

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