Question

A plane turns along a circular, horizontal path (radius r = 600 m) with a speed of 120 m/s, which increases at 5 m/s2. Determine the plane's radial, ar and transverse, a, components of acceleration.

Answer 1

The plane's radial acceleration is 24 m/s^2 and the transverse acceleration is 5 m/s.

Step-by-step explanation:

To determine the plane's radial and transverse components of acceleration, we first need to find the magnitudes of these accelerations.

The radial acceleration, ar, is given by ar = (v^2) / r, where v is the speed of the plane and r is the radius of the circular path.

Substituting the given values, we have ar = (120 m/s)^2 / 600 m = 24 m/s^2.

The transverse acceleration, a, is given by a = d(v) / dt, where d(v) is the change in speed of the plane and dt is the change in time.

Since the speed is increasing at a constant rate, the change in speed is given by dv = a(dt), where a is the acceleration rate and dt is the change in time.

Substituting the given values, we have dv = (5 m/s^2)(1 s) = 5 m/s.

Therefore, the radial acceleration, ar, is 24 m/s^2 and the transverse acceleration, a, is 5 m/s.