Question

The forces on a small airplane (mass 1160 kg) in horizontal flight heading east are as follows: gravity = 16,000 N down; lift = 16,000 N up; thrust = 18,000 N east; and drag = 14,000 N west. The plane's speed is currently 60 m/s. If the forces remain constant, how fast in m/s is the plane going after 10 s?

Answer 1

The final velocity of the plane after 10 seconds is 94.5 m/s east.

Step-by-step explanation:

To calculate the final speed of the plane after 10 seconds, we need to consider the net force acting on the plane. The net force is the vector sum of thrust and drag. Given that the thrust is 18,000 N east and the drag is 14,000 N west, the net force is 18,000 N - 14,000 N = 4,000 N east. We can use Newton's second law, which states that force equals mass times acceleration, to find the acceleration of the plane. The mass of the plane is 1160 kg, so the acceleration is 4,000 N / 1160 kg = 3.45 m/s^2 east. To find the final velocity after 10 seconds, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. The initial velocity is 60 m/s, so the final velocity is 60 m/s + (3.45 m/s^2 east)(10 s) = 60 m/s + 34.5 m/s east = 94.5 m/s east.