A fireman 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of 32.0° 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?

can someone please help me set up this problem?

## Answers (1)

Nice question:

Ok, So first you need to resolve the 40 m/s of the water jet into vertical and horizontal components:

Vertical Component = 40 Sin 32 = 21.20 m/s (We'll need this later)

Horizontal Component = 40 Cos 32 = 33.92 m/s

Ok, so now we can calculate how long it takes the water to travel horizontal to the building which is 50m away.

Speed = Distance/Time. So, Time = Distance/Speed = 50/33.92 = 1.47 s

Now we can calculate how high the water will get in that time:

s = ut + 0.5at^2

Where s is the height reach

u = starting velocity (Thats the vertical component we calculated earlier = 21.20 m/s)

a = accelaration (due to gravity, gravity will be trying to slow the water down so it's a negative number in this case = -9.81 ms^-2)

t = The time from above = 1.47 s)

s = 21.20*1.47 - 0.5*9.81*(1.47)^2

= 31.16 - 10.60

= 20.56 m