Question

You are designing an airport for small planes. One kind of airplane that might use airfield must reach a speed before takeoff of at least 34.0 m/s (100 km/h) and can accelerate at 3.00 m/s². If the runway is 195m long, can this airplane reach the required speed for takeoff? Solve for your known variable.

Answer 1

The airplane can reach a speed of approximately 34.14 m/s, which is greater than the required speed of 34.0 m/s. Therefore, the airplane can reach the required speed for takeoff in the given runway length.

Step-by-step explanation:

To determine if the airplane can reach the required speed for takeoff, we can use the kinematic equation: v^2 = u^2 + 2as where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.

Given that u = 0 m/s (starting from rest), a = 3.00 m/s^2, and s = 195 m, we can solve for v.

Plugging in the values, we get:

v^2 = 0^2 + 2(3.00)(195)

v^2 = 0 + 1170

v = sqrt(1170) = 34.14 m/s

The airplane can reach a speed of approximately 34.14 m/s, which is greater than the required speed of 34.0 m/s. Therefore, the airplane can reach the required speed for takeoff in the given runway length.