Final answer:
The rate at which the plane is gaining altitude can be calculated using trigonometry, specifically the vertical component of the plane's velocity which is the product of the plane's speed and the sine of the lift-off angle.
Step-by-step explanation:
The question asks how fast a plane is gaining altitude if it lifts off from a runway at an angle of 20° with a speed of 300 mph. To find the rate at which the plane is gaining altitude, we can use trigonometry, specifically the sine function because we want the vertical component of the velocity. The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.
Therefore, the rate of altitude gain, or vertical velocity (vvertical), can be calculated using the equation:
vvertical = vplane × sin(θ)
Where:
vplane is the speed of the plane (300 mph)
θ is the angle of ascent (20°)
Inserting the values:
vvertical = 300 mph × sin(20°)
Calculating this gives us the rate at which the plane is gaining altitude.