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MrRissso [65]
3 years ago
8

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks along the x-axis from the spotlight toward the bui

lding at a speed of 1.4 m/s, which is taken as the given dx/dt, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? Step 1
Physics
1 answer:
Assoli18 [71]3 years ago
4 0

Answer:

\frac{dy}{dt}=-4.2m/s

Explanation:

Now, in order to solve this problem we must start by representing it with a drawing. (See attached picture). Notice in the drawing that we are dealing with similar triangles, so we need to build our equation based on the similar equations. So let's build our equation:

\frac{y}{2}=\frac{12}{12-x}

Now, we can solve the equation for y, so we get:

y=\frac{24}{12-x}

now we can differenciate this equation, we can start by turning the fraction into a negative power, like this:

y=24(12-x)^{-1}

Nex we can differenciate the function by using the power and the chain rules, so we get:

\frac{dy}{dt}=-24(12-x)^{-2}(-1)

or:

\frac{dy}{dt}=\frac{24}{(12-x)^{2}} \frac{dx}{dt}

so now we can substitute the values we know:

\frac{dy}{dt}=\frac{24}{(12-4)^{2}} (-1.4)

when solving we get:

\frac{dy}{dt}=-4.2m/s

so the shadow decreases at a rate of -4.2m/s.

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You hold a metal block of mass 40 kg above your head at a height of 2 m.
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Answer:

The work done by gravity is 784 J.

Explanation:

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Now, work done by gravity is equal to the product of force of gravity and the distance moved in the direction of gravity. So,

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3 years ago
At what point in its motion is the KE of a pendulum bob a maximum? 1. The KE does not change. 2. at the lowest point 3. at the h
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Answer:

2. at the lowest point

Explanation:

The motion of the pendulum is a continuous conversion between kinetic energy (KE) and gravitational potential energy (GPE). This is because the mechanical energy of the pendulum, which is sum of KE and GPE, is constant:

E = KE + GPE = const.

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2. at the lowest point

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