What 3 words complete the sentence?<br>A moving object always has energy in its

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.0 ft/s,

natka813 [3]

Answer:

The angle's rate of change is: -0.125 (degree/feet).

Explanation:

In this case of problem we need to find the angle's rate (α) of change when x=6 ft. First we need to relate (α) with x and y and the expression that do it is: $\alpha =Arctan(\frac{y}{x})$ where (α) is the angle between the ladder and the ground, x is the horizontal distance and y the vertical distance, now we need to have the variable y at function of x, so we can do it using the Pythagorean theorem and gets: $y^{2} +x^{2} =10^{2}$ solving for y(x) we get: $y(x)=\sqrt{100-x^{2}}$ . Replacing all we have got in the first equation: $\alpha =Arctan(\frac{\sqrt{100-x^{2} } }{x})$ . Finally we derivate this equation at function of variable x and gets this result: $\frac{d\alpha }{dx} =\frac{-1}{\sqrt{100-x^{2} } }$ evaluating at x=6 ft we get: -0.125(degree/feet). The negative signal means that the angle is decreasing.

4 0

2 years ago

Read 2 more answers

Damian is texting while driving and ends up slamming into the back end of the car in front of him, which then strikes the car in

Sphinxa [80]

The answer for this question is negative externality

3 0

2 years ago

The tension in the rope is constant and equal to 40 N as the block is pulled. What is the instantaneous power (in W) supplied by

Eduardwww [97]

Complete Question:

A 10 kg block is pulled across a horizontal surface by a rope that is oriented at 60° relative to the horizontal surface.

The tension in the rope is constant and equal to 40 N as the block is pulled. What is the instantaneous power (in W) supplied by the tension in the rope if the block when the block is 5 m away from its starting point? The coefficient of kinetic friction between the block and the floor is 0.2 and you may assume that the block starting at rest.

Answer:

Power = 54.07 W

Explanation:

Mass of the block = 10 kg

Angle made with the horizontal, θ = 60°

Distance covered, d = 5 m

Tension in the rope, T = 40 N

Coefficient of kinetic friction, $\mu = 0.2$

Let the Normal reaction = N

The weight of the block acting downwards = mg

The vertical resolution of the 40 N force, $f_{y} = 40sin \theta$

$\sum f(y) = 0$

$N + 40 sin \theta - mg = 0\\N = -40sin60 + 10*9.81 = 0\\N = 63.46 N$

$\sum f(x) = 0$

$40 cos 60 - f_{r} - ma = 0\\ f_{r} = \mu N\\ f_{r} = 0.2 * 63.46\\ f_{r} = 12.69 N\\40cos 60 - 12.69-10a = 0\\7.31 = 10a\\a = 0.731 m/s^{2}$

$v^{2} = u^{2} + 2as\\u = 0 m/s\\v^{2} = 2 * 0.731 * 5\\v^{2} = 7.31\\v = \sqrt{7.31} \\v = 2.704 m/s$

Power, $P = Fvcos \theta$

$P = 40 *2.704 cos60\\P = 54.074 W$

7 0

3 years ago

The period of a pendulum is measured 16 times. The average value of the period over these 16 trials is calculated to be 1.50 sec

marin [14]

Answer:

The additional trials needed is 48 trials

Explanation:

Given;

initial number of trials, n = 16 trials

the standard deviation, σ = 0.24 s

initial standard error, ε = 0.06 s

The standard error is given by;

$\epsilon = \frac{\sigma}{\sqrt{n} }$

To reduce the standard error to 0.03 s, let the additional number of trials = x

$0.03= \frac{0.24}{\sqrt{n+x} } \\\\0.03= \frac{0.24}{\sqrt{16+x} }\\\\0.03\sqrt{16+x} = 0.24\\\\\sqrt{16+x} = \frac{0.24}{0.03} \\\\\sqrt{16+x} = 8\\\\16+x = 8^2\\\\16+x = 64\\\\x = 64 -16\\\\x = 48 \ trials$

Therefore, the additional trials needed is 48 trials.

6 0

3 years ago

Your teacher gives you a piece of cardboard with two pinholes on it, saying that they are separated by 205 μm ± 3%. In order to

wlad13 [49]

Answer:

m,lkj,mkn,njn

Explanation:because she is telling you to do a project

7 0

2 years ago

What 3 words complete the sentence?A moving object always has energy in its​

What 3 words complete the sentence?A moving object always has energy in its