Question

An aircraft is climbing at a 30 degree angle to the horizontal. How fast is the aircraft gaining altitude if it's speed is 500 miles per hour?

Answer 1

Answer:

The aircraft is gaining altitude at $250\frac{mi}{h}$

Explanation:

Draw a vector diagram. (Right angle triangle speed as the hypotenuse)

Let

x -----> horizontal component of the speed

y ----> vertical component of the speed

s ----> speed in miles per hour

we know that

$x=cos(30\°)(s)$

$y=sin(30\°)(s)$

we have

$s=500\ \frac{mi}{h}$

$cos(30\°)=\frac{\sqrt{3}}{2}$

$sin(30\°)=\frac{1}{2}$

substitute

$x=\frac{\sqrt{3}}{2}(500)$

$x=250\sqrt{3}\frac{mi}{h}$

$y=\frac{1}{2}(500)$

$y=250\frac{mi}{h}$

therefore

The aircraft is gaining altitude at $250\frac{mi}{h}$