Final answer:
To determine how long the ski jumper is airborne, we can use the horizontal speed and the angle of the landing incline. By analyzing the horizontal and vertical motions separately, we can find the time in the air. However, without knowing the height of the landing incline, we cannot determine the exact time.
Step-by-step explanation:
To determine how long the ski jumper is airborne, we can use the known horizontal speed of 23 m/s and the angle of the landing incline, which is 43°. Since the ski jumper leaves the ski track moving horizontally, we can treat her motion in the horizontal direction as uniform. This means that the horizontal distance traveled by the ski jumper is equal to the horizontal speed multiplied by the time in the air. To find the time in the air, we can use the equation:
Horizontal distance = Horizontal speed * Time in the air
In this case, the horizontal distance is not given, so we can use the vertical motion of the ski jumper to find it. The vertical motion can be analyzed using the equations of motion under constant acceleration, with the acceleration in the vertical direction being the acceleration due to gravity, 9.8 m/s². Using the equation:
Vertical distance = Vertical initial velocity * Time + (1/2) * Acceleration * Time^2
The vertical distance is the height of the landing incline, which is also not given. However, the vertical initial velocity is 0 m/s, since the ski jumper leaves the ski track horizontally. The vertical distance can be expressed in terms of the height using the equation:
Vertical distance = Height * sin(θ)
Substituting this into the equation for vertical motion, we get:
Height * sin(θ) = (1/2) * Acceleration * Time^2
Simplifying this equation, we find:
Time = sqrt((2 * Height * sin(θ)) / Acceleration)
Plugging in the values given in the problem, we get:
Time = sqrt((2 * Height * sin(43°)) / 9.8)
Since the height is not given, we cannot determine the exact time in the air. Therefore, none of the provided answer choices can be selected.