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3 years ago

10

A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of 6.20×105m/s2 for 8.10×10

-4s. What is its muzzle velocity (that is, its final velocity)?

1 answer:

kati45 [8]3 years ago

7 0

Answer:

502.2 m/s

Explanation:

initial velocity, u = 0 m/s

Let the final speed is v.

acceleration, a = 6.2 x 10^5 m/s^2

time taken, t = 8.10 x 10^-4 s

The muzzle speed is the final speed.

Use first equation of motion

v = u + a t

v = 0 + 6.2 x 10^5 x 8.10 x 10^-4

v = 502.2 m/s

Thus, the muzzle speed of the bullet is 502.2 m/s.

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A swimming pool has the shape of a right circular cylinder with radius 21 feet and height 10 feet. Suppose that the pool is full

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The water required to pump all the water to a platform 2 feet above the top of the pool is is 6061310.32 foot-pound.

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Height = 10 feet

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$V=(441\pi\times\Delta h)\ ft^3$

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Using formula of force

$F=W\times V$

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V = volume

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$F=62.5\times(441\pi\times\Delta h)$

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We need to calculate the work done

Using formula of work done

$W=F\times d$

Put the value into the formula

$W=27562.5\pi\times\Delta h\times(10-h)\ ft\ lbs$

We do this by integrating from h = 0 to h = 10

We need to find the total work,

Using formula of work done

$W=\int_{0}^{h}{W}$

Put the value into the formula

$W=\int_{0}^{10}{27562.5\pi\\times(10-h)}dh$

$W=27562.5\pi(10h-\dfrac{h^2}{2})_{0}^{10}$

$W=27562.5\pi(10\times10-\dfrac{100}{2}-0)$

$W=4329507.37572$

To pump 2 feet above platform, then each slice has to be lifted an extra 2 feet,

So, the total distance to lift slice is (12-h) instead of of 10-h

We need to calculate the water required to pump all the water to a platform 2 feet above the top of the pool

Using formula of work done

$W=\int_{0}^{h}{W}$

Put the value into the formula

$W=\int_{0}^{10}{27562.5\pi\\times(12-h)}dh$

$W=27562.5\pi(12h-\dfrac{h^2}{2})_{0}^{10}$

$W=27562.5\pi(12\times10-\dfrac{100}{2}-0)$

$W=1929375\pi$

$W=6061310.32\ foot- pound$

Hence, The water required to pump all the water to a platform 2 feet above the top of the pool is is 6061310.32 foot-pound.

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