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3 years ago

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A child operating a radio-controlled model car on a dock accidentally steers it off the edge. The car's displacement 0.91 s afte

r leaving the dock has a magnitude of 7.0 m. What is the car's speed at the instant it drives off the edge of the dock?

1 answer:

NemiM [27]3 years ago

6 0

Answer:

Explanation:

distance, d = 7 m

time, t = 0.91 s

speed, v = distance / time

v = 7 / 0.91

v = 7.69 m/s

Thus, the speed is 7.69 m/s

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An airplane accelerates at 16 m/s² from rest. If it lifts off from an aircraft carrier after 6.0 s, how far did it go down the r

Alona [7]

B is the answer
16 x 6.0 = 96
Helping is my pleasure

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2 years ago

A particle with a mass of 0.500 kg is attached to a horizontal spring with a force constant of 50.0 N/m. At the moment t = 0, th

svp [43]

a) $x(t)=2.0 sin (10 t) [m]$

The equation which gives the position of a simple harmonic oscillator is:

$x(t)= A sin (\omega t)$

where

A is the amplitude

$\omega=\sqrt{\frac{k}{m}}$ is the angular frequency, with k being the spring constant and m the mass

t is the time

Let's start by calculating the angular frequency:

$\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{50.0 N/m}{0.500 kg}}=10 rad/s$

The amplitude, A, can be found from the maximum velocity of the spring:

$v_{max}=\omega A\\A=\frac{v_{max}}{\omega}=\frac{20.0 m/s}{10 rad/s}=2 m$

So, the equation of motion is

$x(t)= 2.0 sin (10 t) [m]$

b) t=0.10 s, t=0.52 s

The potential energy is given by:

$U(x)=\frac{1}{2}kx^2$

While the kinetic energy is given by:

$K=\frac{1}{2}mv^2$

The velocity as a function of time t is:

$v(t)=v_{max} cos(\omega t)$

The problem asks as the time t at which U=3K, so we have:

$\frac{1}{2}kx^2 = \frac{3}{2}mv^2\\kx^2 = 3mv^2\\k (A sin (\omega t))^2 = 3m (\omega A cos(\omega t))^2\\(tan(\omega t))^2=\frac{3m\omega^2}{k}$

However, $\frac{m}{k}=\frac{1}{\omega^2}$ , so we have

$(tan(\omega t))^2=\frac{3\omega^2}{\omega^2}=3\\tan(\omega t)=\pm \sqrt{3}\\$

with two solutions:

$\omega t= \frac{\pi}{3}\\t=\frac{\pi}{3\omega}=\frac{\pi}{3(10 rad/s)}=0.10 s$

$\omega t= \frac{5\pi}{3}\\t=\frac{5\pi}{3\omega}=\frac{5\pi}{3(10 rad/s)}=0.52 s$

c) 3 seconds.

When x=0, the equation of motion is:

$0=A sin (\omega t)$

so, t=0.

When x=1.00 m, the equation of motion is:

$1=A sin(\omega t)\\sin(\omega t)=\frac{1}{A}=\frac{1}{2}\\\omega t= 30\\t=\frac{30}{\omega}=\frac{30}{10 rad/s}=3 s$

So, the time needed is 3 seconds.

d) 0.097 m

The period of the oscillator in this problem is:

$T=\frac{2\pi}{\omega}=\frac{2\pi}{10 rad/s}=0.628 s$

The period of a pendulum is:

$T=2 \pi \sqrt{\frac{L}{g}}$

where L is the length of the pendulum. By using T=0.628 s, we find

$L=\frac{T^2g}{(2\pi)^2}=\frac{(0.628 s)^2(9.8 m/s^2)}{(2\pi)^2}=0.097 m$

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3 years ago

A laser source has a bandwidth of 30GHz (a) Calculate the coherence length of the source b) What is the time separation of secti

abruzzese [7]

Explanation:

It is given that,

Bandwidth of a laser source, $f=30\ GHz=30\times 10^9\ Hz$

(b) Let t is the time separation of sections of sections of the light wave that can still interfere. The time period is given by :

$T=\dfrac{1}{f}$

$T=\dfrac{1}{30\times 10^9}$

$T=3.33\times 10^{-11}\ s$

(a) Let h is the coherence length of the source. It is given by :

$l=c\times T$

c is the speed of light

$l=3\times 10^8\times 3.33\times 10^{-11}$

l = 0.0099 m

Hence, this is the required solution.

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2 years ago

The reactive force developed by a jet engine to push an airplane forward is called thrust, and the thrust developed by the engin

finlep [7]

The value of the thrust developed by the engine of a boeing 777 in N and Kgf are ;

i) 376616N

ii) 38430Kgf

<h3>What is force?</h3>

Force is a push or a pull. The reactive force always serve to balance the applied force. We are here asked to convert the the thrust developed by the engine of a boeing 777 which is about 85400 lbf to the following units;

i) N

ii)kgf

Thus;

1 Ib = 0.45 Kg

1 lbf = 0.45 Kg * 9.8 m/s^2 = 4.41 N

We know that;

1 lbf = 4.41 N

85400 lbf = 85400 lbf. * 4.41 N/1 lbf

= 376616N

Again;

1 lbf = 0.45 Kgf

85400 lbf = 85400 lbf * 0.45 Kgf/1 lbf

= 38430Kgf

Learn more about force:brainly.com/question/13191643

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1 year ago

What is force and measurement

NeTakaya

Explanation:

In physics, force is a quantitative description of an interaction that causes a change in an object's motion. ... It is defined as Mass x Acceleration = Force. The SI unit of force is the newton (N); defined as the unit of force which would give to a mass of one kilogram an acceleration of 1 meter per second squared. hope this helps you discover the best answer

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3 years ago