Time to React: Calculating the Pilot's Response

[Brett]

A jet is flying 200 feet above a level plain at 800 mph. Suddenly, the ground begins to rise at a 5 degree slope. How much time does the pilot have to raise the nose before the aircraft strikes the ground?

I came up with (200tan(85))/(800x1.466) seconds. The 1.466 converts the initial velocity from mph to ft/s, and the 200tan(85) is the distance to the point where the 5 degree slope breaks the level plane.

Can anyone double check this and correct me if I made a mistake?

 

[Lyuokdea]

looks good to me, remember you can always check your answer in a problem like this by plugging the answer you get back into a triangle and making sure you get the right answer back via trig.

i.e set up a triangle with one side (800 mph *1.466 ft/s/mph *1.95 seconds) and one with side length 200. both of those units are in meters, so you should be able to use inverse tan to find the angle you get back, does it work?

~Lyuokdea