a fighter plane dives straight down with an acceleration of 3g . what is the magnitude and direction of pilot's effective (or apparent) weight if his real weight is w?

To find the magnitude and direction of the pilot's effective (or apparent) weight, we first need to understand the concept of acceleration and weight.

Acceleration is the rate at which an object changes its velocity. It is usually measured in terms of the acceleration due to gravity (g), which is approximately 9.8 m/s^2 on Earth's surface.

The weight of an object is the force with which it is pulled towards the center of the Earth due to gravity. It is equal to the mass of the object multiplied by the acceleration due to gravity (w = m * g).

In this scenario, the fighter plane is diving straight down with an acceleration of 3g. This means that the plane is experiencing an acceleration three times greater than the acceleration due to gravity.

To determine the pilot's effective weight, we need to consider the forces acting on the pilot. There are two forces at play: the pilot's real weight (w) due to gravity and the force experienced by the pilot as a result of the accelerated motion.

The effective weight of the pilot is the sum of these forces. Since the plane is accelerating downward, the force experienced by the pilot will also be directed downward.

The magnitude of the pilot's effective weight can be calculated using the following formula:

Effective weight = Real weight + Force due to acceleration.

Since the pilot's real weight is w, and the force due to acceleration is equal to the product of the acceleration and the pilot's mass (F = ma), we can rewrite the formula as:

Effective weight = w + ma.

Considering that the plane is accelerating at 3g and the acceleration due to gravity is g, we can substitute the values into the formula:

Effective weight = w + (3g) * m.

Therefore, the magnitude of the pilot's effective weight is (w + 3gm), where m is the mass of the pilot.

The direction of the effective weight will be the same as the direction of acceleration, which in this case is downward. So, the direction of the pilot's effective weight is downward.