What rate is the tip of the shadow moving?
The tip of the shadow is then moving away from the pole at a rate of 3.6923 ft/sec.
What rate is the length of his shadow changing?
Rate of change of shadow is calculated by differentiating length with respect to time. Therefore, the rate at which the length of his shadow is changing is 4 ft/s.
How do you solve problems with involving related rates?
Let’s use our Problem Solving Strategy to answer the question.
- Draw a picture of the physical situation. See the figure.
- Write an equation that relates the quantities of interest. A.
- Take the derivative with respect to time of both sides of your equation. Remember the chain rule.
- Solve for the quantity you’re after.
How fast is the tip of his shadow moving when he is 40ft from the pole?
25 3 ft/s
How fast is the tip of his shadow moving when he is 40 ft from the pole? By similar triangles, 15 y = 6 y−x . That is, 9 y=15 x . dy dt = 25 3 ft/s.
What is the minimum time after which his shadow?
(ii) What is the minimum time after which his shadow will become larger than his original height? The option c) 3 sec is correct.
At what rate is the length of the person’s shadow changing at the moment they are 6 feet tall is their shadow growing or shrinking at that moment?
about 2.917 feet/second
b. [5 points] At what rate is the length of the man’s shadow changing at the moment 6 feet of him are above the ground? Is his shadow growing or shrinking at that moment? ds dt \ \ \ \h=6 = −70 24 = − 35 12 ≈ −2.917 So at that moment, the shadow is shrinking at a rate of about 2.917 feet/second.
Why does the shadow grow taller and shorter?
A person or object blocks more light when the sun is low in the sky. More blocked light makes shadows longer. Less light is blocked when the sun is high in the sky. This makes shadows shorter.
What makes a problem a related rates problem?
A “related rates” problem is a problem in which we know one of the rates of change at a given instant—say, ˙x=dx/dt—and we want to find the other rate ˙y=dy/dt at that instant.
What is a related rates problem?
Related rates problems are word problems where we reason about the rate of change of a quantity by using information we have about the rate of change of another quantity that’s related to it.