Answer to Question #308814 in Mechanics | Relativity for Yza

Question

With its engine cut off, a small airplane glides downward at an angle of 15° below the 

horizontal at a speed of 240 km/h. (a) What are the horizontal and the vertical 

components of its velocity? (b) If the airplane is initially at a height of 2000 m above the 

ground, how long does it take to crash into the ground?  

Note: For (a), you may use m/s or km/h as long as you indicate, and you are consistent 

with the unit that you use. For (b) you may use seconds(s) or minute(m), just indicate the 

unit used.

Answer 1

Explanations & Calculations

a)

• Horizontal component of the velocity is $\small v\cos \theta=240\times\cos 15=231.8\,kmh^{-1}$
• Vertical component is just at the beginning is $\small v\sin\theta=240\sin 15 = 62.1\,kmh^{-1}$

b)

• Since the plane moves in a parabolic trajectory as a projectile it falls under gravitational acceleration.
• Apply $\small s=ut+1/2at^2$ for its downward motion.

$\qquad\qquad \begin{aligned} \downarrow\\ \small s &=\small v\sin\theta\times t+\frac{1}{2}\times(+g)\times t^2\\ \small 2000\,m&=\small \Big(62.1\times\frac{1000m}{3600\,s}\Big)t+\frac{1}{2}\times9.8\,ms^{-2}\times t^2\\ \small 4.9t^2+17.25t-2000&=\small 0\\ \small t&=\small 18.5\quad or \quad -22.0(impossible)\\ \therefore\quad \small t&=\small 18.5\,s \end{aligned}$