Vector/velocity problem?

Question

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

This question is driving me crazy, i just don't know how to do it. Help of any kind is appreciated.

Answer 1

180 km/h = 180 / 3.6 = 50 m/s.

Altitude can be found from traveled distance as h = d sin 32°.  Solving for d, d = h / sin 32° = 1 000 / sin 32° = 1 887 m.  Now, since d = v t, solving for t,

►  t = d / v = 1 887 / 50 = 37.74 s.

Another method:

Vertical component of velocity: 50 sin 32° = 26.5 m/s.  t = altitude / vertical speed, so

►  t = 1 000 / 26.5 = 37.74 s.

Answer 2

The vertical component of the plane's velocity is

[180km/h] sin 32 = 95.39 km/h = 95,385 m/h

1000 / (95,385 m/h) = 0.0105 h = 0.629 min = 37.7 s