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4 years ago

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A basketball rolls onto the court with a speed of 4 . 0 m s 4.0 s m 4, point, 0, space, start fraction, m, divided by, s, end

fraction to the right, and slows down with a constant acceleration of 0 . 5 0 m s 2 0.50 s 2 m 0, point, 50, space, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction over 1 4 m 14m14, space, m. What is the velocity of the basketball after rolling for 1 4 m 14m14, space, m?

1 answer:

svp [43]4 years ago

3 0

Answer:

1.4 m/s

Explanation:

The final velocity of the ball can be found by using the following SUVAT equation:

$v^2-u^2=2ad$

where

v is the final velocity

u is the initial velocity

a is the acceleration

d is the distance travelled

In this problem,

u = 4.0 m/s

d = 14 m

a = -0.50 m/s^2

Solving the equation for v,

$v=\sqrt{u^2+2ad}=\sqrt{4^2+2(-0.50)(14)}=1.4 m/s$

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A 25 kg circular disk has a diameter of 2.5 feet and a thickness of 2.5 cm. Find the density of the disk in kg/m3. Next, find th

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Answer:

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Buoyant force on the disk if it is submerged under water: approximately $\rm 112\; N$ .

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Explanation:

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Diameter: $d = \rm 25\; inches = (25\times 0.3048)\; m = 0.762\;m$ .
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The radius of a circle is 1/2 its diameter:

$\displaystyle r = \rm \frac{1}{2}\times 0.762\;m = 0.381\; m$ .

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$V(\text{disk}) = \pi\cdot r^{2}\cdot h = \pi\times 0.381^{2}\times 0.025 \approx 0.0114009\; m^{3}$ .

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$\displaystyle \rho(\text{disk}) = \frac{m}{V} = \rm \frac{25\; kg}{0.0114009\; m^{3}} = 2.19\times 10^{3}\;kg\cdot m^{-3}$ .

$\rho(\text{disk}) >\rho(\text{water})$ indicates that the disk will sink when placed in water.

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$W(\text{disk}) = m\cdot g = \rm 25\times 9.81 = 245.25\; N$ .

The buoyant force on an object in water is equal to the weight of water that this object displaces. When this disk is submerged under water, it will displace approximately $\rm 0.0114009\; m^{3}$ of water. The buoyant force on the disk will be:

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The size of this disk's weight is greater than the size of the buoyant force on it when submerged under water. As a result, the disk will sink when placed in water.

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