A hot air balloon headed due east at a speed of 20 miles per hour and at a constant altitude of 180 feet passes directly over an intersection. Find an expression for the balloon's distance d (measured in feet) from the intersection t minutes later.
since there are 60 minutes in an hour, the speed can be expressed as 20/60 mi/min = 1/3 mi/min
after t minutes, the distance traveled is thus t/3 miles = 1760t feet
using a right triangle, then it is clear that
d(t) = √(180^2 + (1760t)^2) feet
To find an expression for the balloon's distance from the intersection, we can use the formula for distance: distance = speed * time.
In this case, the speed of the balloon is given as 20 miles per hour, but we need to convert it to feet per minute since the time is given in minutes. There are 5280 feet in a mile and 60 minutes in an hour, so the speed in feet per minute is:
20 miles/hour * 5280 feet/mile / 60 minutes/hour = 1760 feet/minute
Now, let's express the time in minutes. Since the speed is given in feet per minute, we can use the time t in minutes directly.
Therefore, the expression for the balloon's distance d from the intersection t minutes later is:
d = speed * time
d = 1760 * t
So, the expression for the balloon's distance from the intersection t minutes later is 1760t feet.