Distance of hot air balloon from intersection after t seconds

Question

A hot-air balloon, headed due east at an average speed of 15 miles per hour and at a constant altitude of 100 feet, passes over an intersection. Find an expression for the distance d (measured in feet) from the balloon to the intersection t seconds later. (5280 feet in a mile)

Answer 1

Please draw the picture.

You will get right angle triangle

 

Height of triangle =100 ft

other side of triangle is the path of balloon , and that speed is given by 15 miles/hour 

15 miles = 15 * 5280= 79200 feet

15 miles / hr=79200 ft/hr=22 ft/sec

so in t second distance = =22*t=22t

The distance  is the hypotenuse of a right triangle.

 

dist = sqrt[100^2 + (22t)^2]=sqrt[10000+484t^2] feet