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Aethis
23.12.2019 •
Advanced Placement (AP)
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?
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Ответ:
The speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
Since the aircraft is climbing at 30° to the horizontal. it means there will be a vertical component which will be the altitude and also a horizontal component which will be the horizontal distance covered. while the hypotenuse will be how far it has climbed.
Let us call the vertical component x and the hypotenuse component z.
Thus, from trigonometric ratios, we can say that;
sin 30 = x/z
We are looking for how fast the aircraft is gaining altitude. Thus, using Liebniz notation, we can say this rate is; dx/dt. Thus;
sin 30 = (dx/dt)/(dz/dt)
0.5 = (dx/dt)/(dz/dt)
0.5 × (dz/dt) = dx/dt
Its' speed is 500 mph. This means dz/dt = 500
Thus;
dx/dt = 0.5 × 500
dx/dt = 250 mph
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Ответ:
The aircraft is gaining altitude at![250\frac{mi}{h}](/tpl/images/0430/2445/40ace.png)
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
we have
substitute
therefore
The aircraft is gaining altitude at![250\frac{mi}{h}](/tpl/images/0430/2445/40ace.png)
Ответ: