A man 6 feet tall walks at a rate of 5 feet per second toward alight that is 20 feet above the ground. When he is 10 feet from thebase of the light

a) what rate is the tip of his shadow moving?
b) what rate is the length of his shadow changing

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Related questions

How to solve the rate of the tip of the man shadow moving when he is 10 feet from the base of the light? See figure below.

A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground.

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Shadow length A man 6 feet tall walks at a rate of 5 feet per second toward a streetlight that is 30 feet high.

The man's 3-foot-tall child follows at the same speed, but 10 feet behind the man. The shadow behind the child is caused by the man at some times and by the child at other times.

(a) Suppose the man is 90 feet from the streetlight. Show that the man's shadow extends beyond the child's shadow.

(b) Suppose the man is 60 feet from the streetlight. Show that the child's shadow extends beyond the man's shadow.

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Shadow Length A man 6 feet tall walks at a rate of 5 feet per second toward a streetlight that is 30 feet high (see figure). The man’s 3-foot-tall child follows at the same speed, but 10 feet behind the man. The shadow behind the child is caused by the man at some times and by the child at other times.

(a) Suppose the man is 90 feet from the streetlight. Show that the man’s shadow extends beyond the child’s shadow.

(b) Suppose the man is 60 feet from the streetlight. Show that the child’s shadow extends beyond the man’s shadow.

(c) Determine the distance d from the man to the streetlight at which the tips of the two shadows are exactly the same distance from the streetlight.

(d) Determine how fast the tip of the man’s shadow is moving as a function of x, the distance between the man and the streetlight. Discuss the continuity of this shadow speed function.