Question

HI! I need help, this is the complete question but I'm only uncertain about the second part, which formula should I use to solve it?an aircraft is descending with a constant velocity of 133.3m/s at an angle of 2.0 to the horizontal. 1. what is the vertical component of the plane's velocity?2. how long will it take to descend 500m on this flight's path?

Answer 1

Draw a diagram to visualize the situation:

Notice that the vertical component of the velocity can be found using the sine trigonometric function:

$v_y=v\cdot\sin (2º)$

Substitute v=133.3m/s to find the vertical component of the velocity:

$v_y=133.3\frac{m}{s}\times\sin (2º)=4.65\frac{m}{s}$

Use the formula v=d/t to find the time that it takes for the plane to descend 500m. Isolate t:

$\begin{gathered} t=\frac{d}{v} \\ \Rightarrow t=\frac{500m}{4.65\frac{m}{s}}=107.5s \end{gathered}$

Then, the vertical component of the velocity is 4.65m/s (downwards) and it takes 107.5s to descend 500m.