Simple vector problem?

Question

Eh, feel kind of embarrassed asking this, because its supposedly easy, but everything i do is wrong.

A plane taking off leaves the runway at 32degrees to the horizontal, traveling at 180 km/h. How long will it take to climb to an altitude of 1000 m?

Any help is appreciated, cheers :)

Answer 1

You must separate the velocity into vertical and horizontal components. The given speed (180 km/h), along with the veritcal and horizontal components forms a right triangle so the vertical component V can be found from:

sin(32) = V/180 = 0.53

V = (0.53)(180) = 95.36 km/h

You want the time it takes the plane to reach 1000 m (which is just 1 km). This time will be the distance (1 km) divided by the speed of the plane.

time = 1 / 95.36 hours = 0.0105 hours

time = 0.629 minutes

time = 37.74 seconds

Answer 2

This is more of a trig problem

If you draw a right triangle with an angle of 32degrees at one vertex and set the opposite side to a length of 1000m then use the formula

sin (32degrees) = 1000m/hypotenuse

solve for the hypotenuse of the right triangle and this will be the distance that the plane has travelled

hypotenuse = 1887.08m

at 180,000 m/hr (1 km =1000m)

1887.08m/180,000km/hr = .010 hr or 37.74 seconds