Question

A fireman is standing on top of a building 19 m high, holding a firehose 1 m above the top of the building. She finds that if she holds the hose horizontally the water flows from it at 12 m/s. As this happens the water hits an adjacent burning building at a height of 15 m above the ground. (The gravity constant is 9.8 m/s2 . )
What is the horizontal distance from the fireman to the building? (The next page has some additional parts that may help guide you through one potential solution to this problem.)

(a) Do we need to use a vector valued function that is 2-D or 3-D?

(b) What is the acceleration function for the stream of water?

(c) Find the initial velocity, the velocity function, the initial position, and the position function for the stream of water.

(d) How long does it take the water to travel from one building to the other?

(e) What is the horizontal distance from the fireman to the building?

Answer 1

Answer:

A 2 d vector model

The acceleration function is -9.8 m/s2 which is gravity

Initial velocity on the Y axis is 0, on the X axis is 12 m/s

Inital position is 20 mts above the ground.

It takes the water 1.01 seconds to reach the other building.

THe distace from one building to the other is 12.11 meters.

Explanation:

In order to solve this you just need to carefully read the problem and the data you are given, and use the formula for height in free fall:

$h=\frac{1}{2} g*t^{2}$

So first the data, we know that the water is coming out at a height of 20 meters since the building is 19 meters tall and the fireman is holding the firehose 1 meter above it, and the water is hitting the second building at a height of 15 meters, that means that the water is travelin -5meters.

Gravity as it doesn´t say otherwise would be 9.8m/s2 since that is gravity on earth, and water is leaving the firehose at 12m/s horizontally.

We can calculate the time by using the height formula fro free fall:

$h=\frac{1}{2} g*t^{2}\\5=\frac{1}{2} 9.81*t^{2}\\t^{2}= \frac{10}{9.8} \\t^{2}=1.0193\\t=1.009 seconds$

So it takes 1.009 seconds for the water to frop from 20 to 15 meters, as the horizontal velocity remains the same we just multiply it by the time and we get the horizontal distance between the two buildings and that would be:

12.11 meters.