Question

A firefighter, 50.0 m away from a burning building, directs a stream of water from a ground level fire hose at an angle of 30.0° above the horizontal. If the speed of the stream as it leaves the hose is 40.0 m/s, at what height will the stream of water strike the building?

Answer 1

A firefighter, 50.0 m away from a burning building, directs a stream of water from a ground level fire hose at an angle of 30.0° above the horizontal. If the speed of the stream as it leaves the hose is 40.0 m/s, at what height will the stream of water strike the building?

**Solution:**

L = 50m – horizontal range of the stream of water;

V = 40 m/s – speed of the stream of water;

α = 30° – the angle between the stream and the horizontal;

h – building height

Equation of the motion for the stream of water, directed at angle α: (t – time of the flight)

Vₓ = V cos α; Vᵧ = V sin α;

x: L = Vt cos α

t = L/V cos α (1)

y: h = Vt sin α – gt²/2 (2)

(2)in(1)

h = L/V cos α · V sin α – g(L/V cos α)²/2 = L tan α – gL²/2V² cos²α =

= 50m · tan 30° – 9.8 m/s² · 50m/2 · (40 m/s)² · cos 30° = 28.7m

Answer: stream of water will strike the building at height 28.7m