A jet aircraft is accelerating at 4.3 m/s2 as it climbs at an angle of è = 44° above the horizontal (see figure). What is the total force that the cockpit seat exerts on the 77 kg pilot?

To find the total force that the cockpit seat exerts on the pilot, we need to break down the problem into two components: the vertical component and the horizontal component.

1. Vertical Component:
The vertical component of the acceleration is given by:
a_vertical = a * sin(è)
where a is the acceleration and è is the angle of climb.

Substituting the given values, we have:
a_vertical = 4.3 m/s^2 * sin(44°)
a_vertical ≈ 2.92 m/s^2

The weight of the pilot can be calculated using:
Weight = mass * acceleration due to gravity
Weight = 77 kg * 9.8 m/s^2
Weight ≈ 754.6 N

Since the pilot is in equilibrium in the vertical direction, the net vertical force acting on the pilot (including the weight) must be zero. Therefore, the vertical component of the force exerted by the seat must balance the weight.

So, the vertical force exerted by the seat on the pilot is approximately equal to the weight:
Vertical force = 754.6 N

2. Horizontal Component:
The horizontal component of the acceleration can be calculated as:
a_horizontal = a * cos(è)
where a is the acceleration and è is the angle of climb.

Substituting the given values:
a_horizontal = 4.3 m/s^2 * cos(44°)
a_horizontal ≈ 3.1 m/s^2

In the horizontal direction, there is no net force acting on the pilot since there is no acceleration. Therefore, the horizontal force exerted by the seat on the pilot is zero.

3. Total Force:
Finally, we can find the total force by combining the vertical and horizontal components. Since the vertical and horizontal forces act perpendicular to each other, we can use the Pythagorean theorem:
Total force = sqrt((Vertical force)^2 + (Horizontal force)^2)

Substituting the values:
Total force = sqrt((754.6 N)^2 + (0 N)^2)
Total force ≈ 754.6 N

Therefore, the total force that the cockpit seat exerts on the 77 kg pilot is approximately 754.6 Newtons.