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3 years ago

10

A runner accelerates to 4.2 m/s2 for 10 seconds before winning the race. How far did he/she run?

2 answers:

timofeeve [1]3 years ago

8 0

She run the distance of 42metres

hodyreva [135]3 years ago

6 0

Answer:

Runner will run for 210m

Step by Step Explanation:

According to Newton's first of motion,

Vf=Vi+at

Given is

the speed with which runner is running will be Vi, he is running with accelertion a=4.2m/s2 fot time t=10sec

Vf will be 0 because runner will stop after winning the race

we will find Vi from equation 1,

Vi=Vf-at

= 0- 4.2*10

=-42 m/s (negative sign is showing decceleration)

So, Vi=42 m/s

According to Newton's third of motion,

2aS= Vf^2-Vi^2

S is distance, he will cover before stopping,

2(4.2)S= 0- 42^2

S=1764/8.4

S=210m

Runner will run for 210m

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Miss Piggy is exercising her vocal chords by matching the frequency f = 686 Hz of her speaker 4 m away. Where should Kermit sit

monitta

Answer:

$z=\frac{2n+1}{8}$ for $n=0,1,2,3,...,15$

Where z=0 m is the position of Miss Piggy and z=4 m is the position of the speaker.

Explanation:

Assuming that Miss Piggy emits a sound wave that is in phase with the speaker, and that z=0 is the position of Miss Piggy and z=4 is the position of the speaker, we would have a superposition of two traveling sound waves. Furthermore let's assume that both waves have the same amplitude. The total resulting wave will be given by:

$\psi(t,z)=A\cos(\omega t-kz)+A\cos(\omega t +kz)$ where $\omega$ is the angular frequency of the traveling wave and $k$ is the wave number defined as $k=\frac{2\pi}{\lambda}$ . $\lambda$ is the wavelength of both traveling waves (they have the same wavelength because they have the same frequency). $\lambda=\frac{v}{f}$ where v is the speed of sound.

By using the trigonometric identity $2\cos(A)\cos(B)=\cos(A+B)+\cos(A-B)$ we can rewrite $\psi (t,z)$ as

$\psi (t,z)=2A\cos(\omega t)\cos(kz)$ .

In order for the resulting wave to have maximum destructive interference, that is to be zero for any time t, we need to have

$\cos(kz)=0$

$\implies kz=(2n+1)\cdot \frac{\pi}{2}\implies z=(2n+1)\frac{\pi}{2k}=(2n+1)\frac{\pi}{2}\frac{\lambda}{2\pi}=(2n+1)\cdot \frac{\lambda}{4}$

$\implies z=(2n+1)\cdot\frac{v}{4f}=\frac{2n+1}{8}$

3 0

3 years ago

A horizontal 745 N merry-go-round of radius

Arturiano [62]

Answer:

The kinetic energy of the merry-goround after 3.62 s is 544J

Explanation:

Given :

Weight w = 745 N

Radius r = 1.45 m

Force = 56.3 N

To Find:

The kinetic energy of the merry-go round after 3.62 = ?

Solution:

Step 1: Finding the Mass of merry-go-round

$m = \frac{ weight}{g}$

$m = \frac{745}{9.81 }$

m = 76.02 kg

Step 2: Finding the Moment of Inertia of solid cylinder

Moment of Inertia of solid cylinder I = $0.5 \times m \times r^2$

Substituting the values

Moment of Inertia of solid cylinder I

=> $0.5 \times 76.02 \times (1.45)^2$

=> $0.5 \times 76.02\times 2.1025$

=> $79.91 kg.m^2$

Step 3: Finding the Torque applied T

Torque applied T = $F \times r$

Substituting the values

T = $56.3 \times 1.45$

T = 81.635 N.m

Step 4: Finding the Angular acceleration

Angular acceleration , $\alpha = \frac{Torque}{Inertia}$

Substituting the values,

$\alpha = \frac{81.635}{79.91}$

$\alpha = 1.021 rad/s^2$

Step 4: Finding the Final angular velocity

Final angular velocity , $\omega = \alpha \times t$

Substituting the values,

$\omega = 1.021 \times 3.62$

$\omega = 3.69 rad/s$

Now KE (100% rotational) after 3.62s is:

KE = $0.5 \times I \times \omega^2$

KE = $0.5 \times 79.91 \times 3.69^2$

KE = 544J

6 0

4 years ago

Please help! 34 points!

solmaris [256]

I believe the answer is Compression C

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