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Sladkaya [172]
3 years ago
8

A runner of mass 51.8 kg starts from rest and accelerates with a constant acceleration of 1.31 m/s^2 until she reaches a velocit

y of 5.47 m/s. She then continues running at this constant velocity. How long does the runner take to travel 165 m?
Physics
1 answer:
Stells [14]3 years ago
6 0

Answer:32.24 s

Explanation:

Given

mass of runner (m)=51.8 kg

Constant acceleration(a)=1.31 m/s^2

Final velocity (v)=5.47 m/s

Time taken taken to reach 5.47 m/s

v=u+at

5.47=0+1.31\times t

t=\frac{5.47}{1.31}=4.17 s

Distance traveled during this time is

s=ut+\frac{1}{2}at^2

s=\frac{1}{2}\times 1.31\times 4.17^2=11.42 m

So remaining distance left to travel with constant velocity=153.57 m

thus time =\frac{distance}{speed}

t_2=\frac{153.57}{5.47}=28.07 s

Total time=28.07+4.17=32.24 s

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A mass is attached to a vertical spring, which then goes into oscillation. At the high point of the oscillation, the spring is i
andrew-mc [135]

Answer:

0.34 sec

Explanation:

Low point of spring ( length of stretched spring ) = 5.8 cm

midpoint of spring = 5.8 / 2 = 2.9 cm

Determine the oscillation period

at equilibrum condition

Kx = Mg

g= 9.8 m/s^2

x = 2.9 * 10^-2 m

k / m = 9.8 / ( 2.9 * 10^-2 ) =  337.93

note : w = \sqrt{k/m}   = \sqrt{337.93} = 18.38 rad/sec

Period of oscillation =  2\pi  / w

                                  = 0.34 sec

8 0
3 years ago
what happens to the current in a circuit if the resitance of the components in the circuit is increased​
Anit [1.1K]

Answer:

The current decreases.

Explanation:

Current and resistance are inversely proportional. The equation connecting current, resistance and voltage is V = IR, where V is voltage, I is current and R is resistance.

Rearranging this equation, you get:

I = \frac{V}{R}

and

R = \frac{V}{I}

If the value of voltage in both equations remains constant, and the value of R decreases, the value of I will increase. Conversely, if in the second equation R = \frac{V}{I} , the value of V remains constant the value of I decreases, then the value of R, resistance will increase.

Thus, it can be seen that the current will decrease as resistance increases and vice versa.

7 0
3 years ago
A mortar is like a small cannon that launches shells at steep angles. A mortar crew is positioned near the top of a steep hill.
Elena-2011 [213]

1) Distance down the hill: 1752 ft (534 m)

2) Time of flight of the shell: 12.9 s

3) Final speed: 326.8 ft/s (99.6 m/s)

Explanation:

1)

The motion of the shell is a projectile motion, so we  can analyze separately its vertical motion and its horizontal motion.

The vertical motion of the shell is a uniformly accelerated motion, so the vertical position is given by the following equation:

y=(u sin \theta)t-\frac{1}{2}gt^2 (1)

where:

u sin \theta is the initial vertical velocity of the shell, with u=156 ft/s and \theta=49.0^{\circ}

g=32 ft/s^2 is the acceleration of gravity

At the same time, the horizontal motion of the shell is a uniform motion, so the horizontal position of the shell at time t is given by the equation

x=(ucos \theta)t

where u cos \theta is the initial horizontal velocity of the shell.

We can re-write this last equation as

t=\frac{x}{u cos \theta} (1b)

And substituting into (1),

y=xtan\theta -\frac{1}{2}gt^2 (2)

where we have choosen the top of the hill (starting position of the shell) as origin (0,0).

We also know that the hill goes down with a slope of \alpha=-41.0^{\circ} from the horizontal, so we can write the position (x,y) of the hill as

y=x tan \alpha (3)

Therefore, the shell hits the slope of the hill when they have same x and y coordinates, so when (2)=(3):

xtan\alpha = xtan \theta - \frac{1}{2}gt^2

Substituting (1b) into this equation,

xtan \alpha = x tan \theta - \frac{1}{2}g(\frac{x}{ucos \theta})^2\\x (tan \theta - tan \alpha)-\frac{g}{2u^2 cos^2 \theta} x^2=0\\x(tan \theta - tan \alpha-\frac{gx}{2u^2 cos^2 \theta})=0

Which has 2 solutions:

x = 0 (origin)

and

tan \theta - tan \alpha=\frac{gx}{2u^2 cos^2 \theta}=0\\x=(tan \theta - tan \alpha) \frac{2u^2 cos^2\theta}{g}=1322 ft

So, the distance d down the hill at which the shell strikes the hill is

d=\frac{x}{cos \alpha}=\frac{1322}{cos(-41.0^{\circ})}=1752 ft=534 m

2)

In order to find how long the mortar shell remain in the air, we can use the equation:

t=\frac{x}{u cos \theta}

where:

x = 1322 ft is the final position of the shell when it strikes the hill

u=156 ft/s is the initial velocity of the shell

\theta=49.0^{\circ} is the angle of projection of the shell

Substituting these values into the equation, we find the time of flight of the shell:

t=\frac{1322}{(156)(cos 49^{\circ})}=12.9 s

3)

In order to find the final speed of the shell, we have to compute its horizontal and vertical velocity first.

The horizontal component of the velocity is constant and it is

v_x = u cos \theta =(156)(cos 49^{\circ})=102.3 ft/s

Instead, the vertical component of the velocity is given by

v_y=usin \theta -gt

And substituting at t = 12.9 s (time at which the shell strikes the hill),

v_y=(156)(cos 49^{\circ})-(32)(12.9)=-310.4ft/s

Therefore, the  final speed of the shell is:

v=\sqrt{v_x^2+v_y^2}=\sqrt{(102.3)^2+(-310.4)^2}=326.8 ft/s=99.6 m/s

Learn more about projectile motion:

brainly.com/question/8751410

#LearnwithBrainly

5 0
3 years ago
When reaching a boundary between two media (1 and 2), an incident ray is partially reflected and partially refracted. The ray is
podryga [215]

Answer: critical angle, sin^-1 (n2/n1)

Explanation: the angle of incidence at which the retracted ray makes an angle of 90° with the normal is known as the critical angle.

Snell's law defined refraction mathematically as shown below

n1 sin θi = n2 sin θr

n1 = refractive index of the first medium

n2 = refractive index of the second medium

θi = angle of incidence

θr = angle of refraction

When the refrafted ray is perpendicular to the normal, the angle of refraction (θr) is 90° hence making the angle of incidence (θi) the critical angle θc

By substituting these conditions into the Snell's law, we have that

n1 sin θc = n2 sin 90

According to trigonometry, the value of sin 90 is 1, hence we have that

n1 sin θc =n2

sin θc = n2/n1

θc = sin^-1 (n2/n1)

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3 years ago
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Yes. If a downward force is created, it will be felt at the end of the rope as well.

3 0
3 years ago
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