Question

A military plane is flying directly toward an air traffic control tower, maintaining an altitude of 9 miles above the tower. The radar detects that the distance between the plane and the tower is 15 miles and that it is decreasing at a rate of 750mph. What is the ground speed of the plane

Answer 1

-937.5 mph

Explanation:

Assuming this takes place in a right angled triangle. With the hypotenuse side being, d, 15 miles, the opposite side being 9 miles and the adjacent being an unknown, x.

Using Pythagoras theorem, we know that

x² = 15² - 9²

x² = 225 - 81

x² = 144

x = √144

x = 12 miles.

Again, we should know that

2xx' = 2dd', this means that

xx' = dd'

From the question, we're told that it's decreasing at d' = 750 mph. On substituting, we have

x' = dd' / x

x' = (15 * -750) / 12

x' = -11250 / 12

x' = -937.5 mile per hour

The ground speed of the plane is also decreasing at 937.5 mile per hour