An airplane of mass 2800 Kg has just lifted off the runway. It is gaining altitude at a constant 2.3 M/s while the horizontal component of its velocity is increasing at a rate of 0.86 M/s2. Assume g= 9.81 M/s2. (a) Find the direction of the force exerted on the airplane by the air. (b) Find the horizontal and vertical components of the planes acceleration if the force due to the air has the same magnitude but has a direction of 2.0ᴼ closer to the vertical than its description in part (a).
To answer both parts of the question, we need to understand the forces acting on the airplane.
(a) The force exerted on the airplane by the air can be split into two components: lift and weight.
1. Lift: This is the force generated by the wings of the airplane in order to counteract gravity and allow the airplane to gain altitude. Since the airplane is gaining altitude at a constant rate, the lift force must be equal to the weight of the airplane.
2. Weight: This is the force due to gravity acting on the airplane and can be calculated using the equation: weight = mass * gravity. In this case, weight = 2800 kg * 9.81 m/s^2.
The direction of the force exerted on the airplane by the air is opposite to the gravitational force (downward) since the lift force needs to counteract it.
(b) In this part, the magnitude of the force due to air remains the same as in part (a), but its direction is changed. Let's calculate the horizontal and vertical components of the plane's acceleration:
1. Horizontal component of acceleration: The increase in the horizontal component of velocity, which is 0.86 m/s^2, tells us that there must be a horizontal force acting on the airplane. This force is responsible for accelerating the airplane horizontally. We can calculate the horizontal component of acceleration using the formula: horizontal acceleration = force / mass. Plug in the known values to find the horizontal acceleration.
2. Vertical component of acceleration: The airplane is gaining altitude at a constant rate of 2.3 m/s. This rate of change of velocity vertically is the vertical component of acceleration. It is independent of the force exerted by air since we're assuming the magnitude of the force is the same as in part (a). Therefore, the vertical component of acceleration remains 2.3 m/s.
Overall, the horizontal component of acceleration found in part (b) will differ from the horizontal component of acceleration found in part (a), due to the changed direction of the force exerted by the air.