Problem 48.

Problem 4.14 of Serway & Jewett: A firefighter, a distance d from a burning building,
directs a stream of water from a fire hose at angle above the horizontal. If the initial
speed of the stream is , at what height h does the water strike the building?

Solution:

This is the projectile motion. The equation which describe the motion along horizontal axis x is the following

where is the x-component of initial velocity.

Along axis y we have motion with constant acceleration:

In these equations at the initial moment of time the water has zero coordinate.

What do we know about the final point: we know only the x-coordinate of the final point – it is x=d. We can substitute this coordinate in the first equation (which describe the motion along axis x):

From this equation we can find the traveled time:

Then we substitute this time into the equation which describe the y-coordinate of the water:

This expression gives as the height where the water strikes the building.