Question

An airplane is taking off at angle of 9 degrees and traveling at a speed of 200 feet per second in relation to the ground. If the clouds begin at an altitude of 4,000 feet, how many seconds will it take for the airplane to be in the clouds?

Answer 1

`\begin{equation*} 127.85\text{ }seconds \end{equation*}`

Step-by-step explanation

First, let us make a sketch of the problem:

To find the time it will take the airplane to be in the clouds, we first have to find the distance flown by the airplane in attaining that height, x.

To do this, apply trigonometric ratios SOHCAHTOA for right triangles:

`\sin9=(4000)/(x)`

Solve for x:

`\begin{gathered} x=(4000)/(\sin9) \\ x=25,569.81\text{ }ft \end{gathered}`

Now, that we have the distance, we can solve for the time by applying the relationship between speed and distance:

`\begin{gathered} speed=(distance)/(time) \\ \Rightarrow time=(distance)/(speed) \end{gathered}`

Substitute the given values into the formula above and solve for time:

`\begin{gathered} time=(25569.81)/(200) \\ time=127.85\text{ }seconds \end{gathered}`

That is the number of seconds that it will take.