An airplane is flying in still air with an airspeed of 325 miles per hour. If it is climbing at an angle of 20°, find the rate at which it is gaining altitude.
Make sure your calculator is in DEGREE mode
sin(20)(325)= 111.16
Finding the derivative gives you the same answer, but we have to the set our calculators to degree and not radian in order to solve it the way anonymous did.
To find the rate at which the airplane is gaining altitude, we can use trigonometry. The vertical component of the airplane's velocity represents the rate at which it is gaining altitude.
Let's break down the problem into components:
1. The airspeed of the airplane represents the total velocity (both horizontal and vertical) of the airplane.
2. The vertical component of the airplane's velocity can be found using the sine function (which relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle).
Since the angle of climb is given as 20°, we can calculate the rate at which the airplane is gaining altitude as follows:
1. Calculate the vertical component of the velocity using the sine function: sin(20°) = opposite/hypotenuse = vertical velocity/325 mph.
vertical velocity = 325 mph * sin(20°).
2. Now we have the rate at which the airplane is gaining altitude.
Using a calculator, we can calculate the value of sin(20°) as approximately 0.342.
Therefore, the rate at which the airplane is gaining altitude is approximately 325 mph * 0.342 = 111.45 mph.
So, the airplane is gaining altitude at a rate of approximately 111.45 mph.
dude ur supposed to take the derivative
why are people disliking Anonymous' answer? it's correct.
because it's wrong
You're going to use sin = 0pposite / Hypotenuse.
In this case the hypotenuse is 325 mph, the opposite side is the gain in altitude, 20 degrees is your angle.
Therefore sin 20 = Opposite / 325 mph
sin 20 * 325 = Opposite
111.15 mph = opposite
The airplane is climbing at a rate of 111.15 mph