Question #1730

A fire fighter, 50.0 m away from a building ,directs a stream of water from a firehouse at an angle of 30 degrees above the horizontal as in the figure below. If the initial speed of the stream is 40m/s, at what height does the water strike the building?

Expert's answer

I. Let's consider the motion by projections:

Horizontal: s = v_{0} cos(30) t

Vertical: h = v_{0} sin(30)t - gt^{2}/2

t = s/v_{0} cos(30) = 50/40* (√3/2) = 1.44 s

h = 40*1/2 * 1.44 - 10*1.44^{2}/2 = 18.38 m

Answer: 18.4 m

Horizontal: s = v

Vertical: h = v

t = s/v

h = 40*1/2 * 1.44 - 10*1.44

Answer: 18.4 m

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