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December 18, 2014

December 18, 2014

Posted by **Josh** on Sunday, September 17, 2006 at 1:30am.

:) Thanks.

Firemen are shooting a stream of water at a burning building. A high-pressure hose shoots out the water with a speed of 21.0 m/s as it leaves the hose nozzle. Once it leaves the hose, the water moves in projectile motion. The firemen adjust the angle of elevation of the hose until the water takes 3.00 s to reach a building 35.0 m away. You can ignore air resistance; assume that the end of the hose is at ground level.

Find the angle of elevation of the hose.

Don't know...

Find the speed of the water at the highest point in its trajectory.

Don't know...

Find the acceleration of the water at the highest point in its trajectory.

Don't know...

How high above the ground does the water strike the building?

Don't know...

How fast is it moving just before it hits the building?

Don't know...

You should know the answer to the thrid part at least, since the water follows projectile motion. All projectiles accelerate toward the ground with rate equal to g.

The time that it takes for the water to reach the fire, and the distance D, can be used to tell you the horizontal component of the water velocity leaving the hose, Vo cos A.

(Vo cos A) * (3 seconds) = D

Since the exit velocity Vo is 21 m/s, solve for the cosine of the elevation angle A. From that, get A itself.

At the highest point of the trajectory, the vertical component of velocity is zero, and the horizontal component rmeains the initial value.

Use the initial vertical component Vo sin A to compute how high it goes. It will spend t = 1.50 seconds going up. The height reached is

H = Vo sin A * t - (1/2) gt^2.

For the last part (final velocity) think about applying conservation of energy. The potential energy has not changed.

Please use these hints to make progress on the problem.

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