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Question 53765: A hot air balloon is headed due east at a constant altitude of 200 feet, going 30 mph steady speed. It passes over Rover the dog, who is sitting still. Find an expression for the distance (in feet) from Rover to the balloon as a function of time (in seconds).
I figured out that 30 mph= 44.02 feet per second.
Also, I know to use the pythag thereom, but I can't simplify it from there. Help!
Found 2 solutions by Earlsdon, venugopalramana:
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Well, you are correct in assuming that you will need to use the Pythagorean theorem.
You can draw a diagram of this situation and it will look like an inverted right triangle, won't it?
Rover will be located at the vertex opposite the base of the triangle.
The leg of the triangle will be the distance from Rover on the ground to the line-of-flight of the balloon (200 ft.)
The base of the triangle can be written as a function of time because you would want it to be a distance, and d = rt, where r = 44 ft/sec. and t = time. The the length of the base of the inverted right triangle would be: 44(t).
Now you can write the expression for the distance from Rover to the balloon as a function of time, t. In your diagram, this would be the hypotenuse (d for distance) of the inverted right triangle. So the expression for d becomes:
 Simplify.
Answer by venugopalramana(3286)  (Show Source):
You can put this solution on YOUR website! A hot air balloon is headed due east at a constant altitude of 200 feet, going 30 mph steady speed. It passes over Rover the dog, who is sitting still. Find an expression for the distance (in feet) from Rover to the balloon as a function of time (in seconds).
I figured out that 30 mph= 44.02 feet per second.
Also, I know to use the pythag thereom, but I can't simplify it from there. Help!
LET ROVER BE AT R ON GROUND.
LET V BE THE VERTICAL POSITION OF BALLOON FROM ROVER.
LET THE BALLON BE AT P AFTER T SECS.
TRIANGLE VRP IS RIGHT ANGLED AT R.HENCE
RP^2 = RV^2+VP^2
RV= 200'
VP = TIME * VELOCITY = T*30 MPH =T*30*22/15 = 44T FT
RP^2 = 200^2+(44T)^2=40000+1936T^2
RP = [1936T^2+4000}60.5
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