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1 year ago

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Consider a basketball player spinning a ball on the tip of a finger. If a player performs 1.91 J1.91 J of work to set the ball s

pinning from rest, at what angular speed ????ω will the ball rotate? Model a basketball as a thin-walled hollow sphere. For a men's basketball, the ball has a circumference of 0.749 m0.749 m and a mass of 0.624 kg0.624 kg .

1 answer:

Black_prince [1.1K]1 year ago

7 0

Answer:

ω = 4.07 rad/s

Explanation:

By conservation of the energy:

W = ΔK

$1.91J = I/2*\omega^2$

where $I = 2/3*m*R^2=0.23kg.m^2$

Solving for ω:

$\omega = \sqrt{W*2/I} =4.07rad/s$

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A weather balloon is rising vertically from a launching pad on the ground. A technician standing 300 feet from the launching pad

avanturin [10]

Answer:

$\dfrac{dh}{dt} =5\ ft/s$

Explanation:

Let

h = height of balloon (in feet).

θ = angle made with line of sight and ground (in radians).

h = 300 tanθ

$\dfrac{dh}{d\theta } = 300 sec^2\theta$

now $\dfrac{dh}{dt}$ can be written as

$\dfrac{dh}{dt} =\dfrac{dh}{d\theta }\times \dfrac{d\theta }{dt}$

$\dfrac{d\theta }{dt} = \dfrac{1}{120}\at \ \theta =\dfrac{\pi}{4}$

When θ = π/4,

$\dfrac{dh}{d\theta } = 300 sec^2\theta$

$\dfrac{dh}{d\theta } = 600$

$\dfrac{dh}{dt} =\dfrac{dh}{d\theta }\times \dfrac{d\theta }{dt}$

$\dfrac{dh}{dt} =600\times \dfrac{1}{120}$

$\dfrac{dh}{dt} =5\ ft/s$

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1 year ago

The net force on a boat causes it to accelerate at 1.55 m/s2. The mass of the boat is 215 kg. The same net force causes another

jekas [21]

Answer:

2666 kg

0.11567 m/s²

Explanation:

m = Mass of boat

a = Acceleration of boat

From Newton's second law

Force

$F=ma\\\Rightarrow F=215\times 1.55\\\Rightarrow F=333.25\ N$

Force on the first boat is 333.25 N

$F=ma\\\Rightarrow m=\frac{F}{a}\\\Rightarrow m=\frac{333.25}{0.125}\\\Rightarrow m=2666\ kg$

Hence, mass of the second boat is 2666 kg

Combined mass = 2666+215 = 2881 kg

$F=ma\\\Rightarrow a=\frac{F}{m}\\\Rightarrow a=\frac{333.25}{2881}\\\Rightarrow a=0.11567\ m/s^2$

The acceleration on the combined mass is 0.11567 m/s²

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1 year ago

A bird flies at an average velocity of 3.60 m/s for 18.4 s. How far does it travel? (unit=m)

jarptica [38.1K]

First, you have to write what you know:

V = 3.60 m/s
D = ?
T = 18.4 s

Next, you plug everything into this formula:

V = D/T
3.60 m/s = ?/18.4 s

Then, you multiply 3.60 m/s and 18.4 s

D = 66.24 m

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1 year ago

Suppose a convex mirror has a focal length of 120 cm. A candle sits directly in front of the mirror. If the image of that candle

Andru [333]

We can solve the problem by using the mirror equation:
$\frac{1}{f} = \frac{1}{d_o}+ \frac{1}{d_i}$
where
f is the focal length
$d_o$ is the distance of the object from the mirror
$d_i$ is the distance of the image from the mirror

For the sign convention, the focal length is taken as negative for a convex mirror:
$f=-120 cm$
and the image is behind the mirror, so virtual, therefore its sign is negative as well:
$d_i=-24 cm$
putting the numbers in the mirror equation, we find the distance of the object from the mirror surface:
$\frac{1}{d_o} = \frac{1}{f}- \frac{1}{d_i}= \frac{1}{-120 cm} - \frac{1}{-24 cm}= \frac{1}{30 cm}$
So, the distance of the object from the mirror is $d_o = 30 cm$

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1 year ago

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Lunna [17]

1. Physical size of Russia compared to other countries, despite a lack of visible borders from space.

2. Part of Russia's outline would likely be obscured by the various clouds and objects in the stratosphere; this would allow the astronaut to view potential cloud and weather patterns on earth.

3. An astronaut could see outlines of Russia's geography such as mountain ranges.

Hope that it helps :)

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1 year ago