A person 1.8m tall is walking away from a lamppost 6m high at the rate 1.3m/s. At what rate is the end of the person's shadow moving away from the lamppost?
the point of what follows and the choice of variables in the drawing is this. we know that
so similar triangles tells us that
and now for the little bit of calculus, taking the deriv of each side with respect to time
By signing up, you agree to our Terms of Service and Privacy Policy
To find the rate at which the end of the person's shadow is moving away from the lamppost, we can use similar triangles. Let's denote:
( h_p ) = height of the person (1.8m)
( h_l ) = height of the lamppost (6m)
( x ) = distance from the person to the lamppost (the length of the shadow)
Given that the person is walking away from the lamppost at a rate of ( 1.3 , \text{m/s} ), we need to find ( \frac{dx}{dt} ), the rate at which the shadow's end is moving away from the lamppost.
Using similar triangles, we have:
[ \frac{h_l}{x} = \frac{h_p}{x + h_p} ]
Differentiating both sides with respect to time ( t ):
[ -\frac{h_l}{x^2}\frac{dx}{dt} = -\frac{h_p}{(x + h_p)^2}\frac{dx}{dt} ]
Given ( h_l = 6 , \text{m} ), ( h_p = 1.8 , \text{m} ), and ( \frac{dx}{dt} = 1.3 , \text{m/s} ), we can solve for ( \frac{dx}{dt} ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you find the point on the line #y=4x + 7# that is closest to the point (0,-3)?
- A ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes How fast is a rider rising when the rider is 16 m above ground level?
- How do you use Newton's method to find the approximate solution to the equation #x+1/sqrtx=3#?
- What is the local linearization of #F(x) = cos(x) # at a=pi/4?
- How do you minimize and maximize #f(x,y)=(e^(yx)-e^(-yx))/(2yx)# constrained to #1<x^2/y+y^2/x<3#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7