Question

A jet ascends at a 10 degree angle from the horizontal with an airspeed of 550 mi/hr (its speed along its line of flight is 550 mi/hr). How fast is the altitude of the jet increasing? If the sun is directly overhead, how fast is the shadow of the jet moving on the ground?

Answer 1

1) Consider the departure point is A (0,0).
After one hour flight with an angle of elevation of 10°, it travelled a distance of 550 mi. (speed 550 mi/h) and reached an altitude of H.
(Imagine a right triangle: Departure point A (0,0), with angle of elevation A= 10° and after one hour reaching a point B, at an altitude H, note that AB = hypotenuse-)

Let's calculate H (after 1 hour/flight)

sin10° = H/AB = H/550 and H= 95.5065 mi, Speed of H = 95.506 mi/h

2) The shadow is represented by the horizontal side, adjacent to 10°.

So when the plane is advancing at 550 mi/h, the shadow is stretched at a speed S.
Now let's calculate the length of the shadow (always after one hour flight)
Pythagoras: 550² =95.5065² +(length of shadow)²
And Length of shadow = 541.65 mi
S= 541.65/1 hour = 541.65 mi/h