Find the speed of the plane?

Question

A high-performance jet plane, practicing radar avoidance maneuvers, is in horizontal flight 35.0 m above the level ground. Suddenly, the plane encounters terrain that slopes gently upward at 4.10°, an amount difficult to detect. How much time does the pilot have to make a correction to avoid flying into the ground ( s)? The speed of the plane is 1250 km/h.

Answer 1

Suppose the plane is at a distance X when he encounters the terrain. Take a pen and paper, Draw a right angled triangle with Base AB=X and Perpendicular BC and then your pilot would be above point A.

Also the angle BAC is 4.10 deg

Since you know how much the perpendicular BC is (35.0m) since that's where the pilot is above point A, using trigonometry you can calculate the base AB as BC cot(4.10) which = 35Cot(4.10) m

Now the pilot has this much distance to adjust as you can see from the diagram you drew the closer he moves to perpendicular his height decreases and at point C he will collide with ground.

Now you know his speed his 1250Km/hr therefore time required to cover this distance would be

35 Cot(4.10) = (1250*5)/18 t ( I multiplied 1250 by fraction 5/18 to convert KM/hr into m/s)

Calculate t to get your result.