A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously m
easure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 18° and 20°. How high is the balloon? (Round your answer to one decimal place.)
1 answer:
Answer:
3.1 miles
Explanation:
To solve this question it is important to remember that the distance between two mile markers is approximately 1 mile
Once this is known, the question becomes very easy to solve. We make two triangle, which have the following three points
Triangle 1: Hot-Air-Balloon, Ground, Milepost 1 - With angle of depression 20
Triangle 2: Hot-Air-Balloon, Ground, Milepost 2 - With angle of depression 18
As a reminder, the angle of depression is simply the angle the balloonist's head makes with the horizontal plane to be able to see the milepost.
From this we can simply drive two formulas using the Tan function
Equation 1 -
Equation 2 -
Solving them simultaneously we get the value of height (h) to be 3.0852 miles or 3.1 miles
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Missing details: figure of the problem is attached.
We can solve the exercise by using Poiseuille's law. It says that, for a fluid in laminar flow inside a closed pipe,
where:
is the pressure difference between the two ends
is viscosity of the fluid
L is the length of the pipe
is the volumetric flow rate, with
being the section of the tube and
the velocity of the fluid
r is the radius of the pipe.
We can apply this law to the needle, and then calculating the pressure difference between point P and the end of the needle. For our problem, we have:
is the dynamic water viscosity at
L=4.0 cm=0.04 m
and r=1 mm=0.001 m
Using these data in the formula, we get:
However, this is the pressure difference between point P and the end of the needle. But the end of the needle is at atmosphere pressure, and therefore the gauge pressure (which has zero-reference against atmosphere pressure) at point P is exactly 3200 Pa.
