A firefighter 50.0 m away from a burning building directs a stream of water from a fire hose at an angle of 30° above the horizontal. If the velocity stream is 40.0 m/s, at what height will the stream of water strike the building?

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Answer 1 · 2017-02-17T17:49:11

The water will strike the building at a height of 18.6 m.

MFDocs

We can get the time of flight from the horizontal component:

#sf(Vcostheta=s/t)#

#:.##sf(t=s/(Vcostheta)=50/(40cos30)=50/(40xx0.866)=1.44color(white)(x)s)#

For the vertical component we can use:

#sf(h=ut+1/2at^2)#

This becomes:

#sf(h=40sin30t-1/2"g"t^2)#

#:.##sf(h=20xx1.44-1/2xx9.81xx2.073)#

#sf(h=28.8-10.17=18.63color(white)(x)m)#