How would you solve this problem:
An airplane is flying in still air with an airspeed of 240 mph. If it is climbing at an angle of 22 degrees, find the rate at which it is gaining altitude.
need help
To solve this problem, we can use trigonometry to find the rate at which the airplane is gaining altitude.
Let's break down the information given:
1. The airspeed of the plane is 240 mph.
2. The plane is climbing at an angle of 22 degrees.
We can use the concept of trigonometry to relate the horizontal and vertical components of the airplane's motion.
The horizontal component is the airspeed of the plane since it is flying in still air. The vertical component is the rate at which it is gaining altitude.
First, let's find the vertical component using trigonometry. In a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse.
In this case, the angle of climb (22 degrees) is the angle opposite to the vertical component, and the airspeed (240 mph) is the hypotenuse of the right triangle. Let's use the formula:
sin(angle) = opposite / hypotenuse
Applying this formula, we have:
sin(22 degrees) = vertical component / 240 mph
Now, let's solve for the vertical component:
vertical component = sin(22 degrees) * 240 mph
Using a calculator, we can find the value of sin(22 degrees) to be approximately 0.3746. Therefore, the vertical component (rate at which the airplane is gaining altitude) is:
vertical component = 0.3746 * 240 mph
Calculating this value, we find that the rate at which the airplane is gaining altitude is approximately 89.9 mph.