Question

An airplane leaves the runway with a velocity of 70 m/s while climbing at an angle of 30 degrees to the horizontal. What is the vertical speed of the airplane?

A) 30 m/s
B) 35 m/s
C) 40 m/s
D) 45 m/s

Answer 1

To determine the vertical speed of an airplane climbing at an angle, we use trigonometric functions to calculate the vertical component of the velocity. The correct vertical velocity for the airplane climbing at a 30-degree angle with a total speed of 70 m/s is 35 m/s.

Step-by-step explanation:

The subject of the question is Physics, specifically dealing with the components of velocity in projectile motion. To find the vertical speed of the airplane, we can use trigonometric functions to resolve the total velocity into its vertical component. The vertical speed (Vy) is given by Vy = Vtotal × sin(θ), where Vtotal is the total velocity (70 m/s) and θ is the angle of ascent (30 degrees). Using this formula, Vy = 70 m/s × sin(30 degrees), which equals 70 m/s × 0.5, hence the vertical velocity is 35 m/s. Therefore, the correct answer is B) 35 m/s.