SOLUTION: A PLANE TAKES OFF AT 19 DEGREES AT SPEED OF 300 METERS PER HOUR. HOW LONG WILL IT TAKE TO REACH A HEIGHT OF 1000 ft.?

Algebra ->  Trigonometry-basics -> SOLUTION: A PLANE TAKES OFF AT 19 DEGREES AT SPEED OF 300 METERS PER HOUR. HOW LONG WILL IT TAKE TO REACH A HEIGHT OF 1000 ft.?      Log On


   

Question 247116: A PLANE TAKES OFF AT 19 DEGREES AT SPEED OF 300 METERS PER HOUR. HOW LONG WILL IT TAKE TO REACH A HEIGHT OF 1000 ft.?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
sin(19) = o/h = 1000/h

h = 1000/sin(19) = 3071.553487 feet

looks like your mixing feet and meters.

If so, then we have to convert 3071.553487 feet to meters, or convert 300 meters to feet.

I'll convert 300 meters to feet.

1 meter = 3.2808399 feet

300 meters = 300 * 3.2808399 = 984.251969 feet

The plane is traveling at 984.251969 feet per hour.

The plane travels 3071.553487 feet to reach an altitude of 1000 feet.

It takes the plane 3071.553487 / 984.251969 = 3.120698341 hours to reach a height of 1000 feet.

I don't think you meant 300 meters per hour.

I believe you meant 300 miles per hour.

That changes the equation drastically.

There are 5280 feet in a mile.

300 miles per hours translates to 1584000 feet per hour.

The plane is traveling at 1584000 feet per hour.

The plane travels 3071.553487 feet to reach an altitude of 1000 feet.

It takes the plane 3071.553487 / 1584000 = .001939112 hours to reach a height of 1000 feet.

That would be equivalent to .116346723 minutes to reach a height of 1000 feet.

That would be equivalent to 6.98080338 seconds to reach a height of 1000 feet.

The speed of the plane is measured in relationship to the direction it is traveling. That direction is along the line of the hypotenuse of the right triangle formed by the 19 degrees.