Answer to Question #1730 in Mechanics | Relativity for qolani sambo

Question

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?

Answer 1

I. Let's consider the motion by projections:
Horizontal: s = v₀ cos(30) t
Vertical: h = v₀ sin(30)t - gt²/2

t = s/v₀ cos(30) = 50/40* (√3/2) = 1.44 s
h = 40*1/2 * 1.44 - 10*1.44²/2 = 18.38 m
Answer: 18.4 m