Final answer:
The magnitude of the force on the rider by the sled is approximately 936.33 N.
Step-by-step explanation:
To calculate the force on the rider by the sled, we need to consider the horizontal and vertical components of acceleration. The horizontal component of acceleration is 5.0 m/s² and the downward component is 3.8 m/s². Additionally, we need to account for the gravitational acceleration, which is 9.8 m/s². The total acceleration in the horizontal direction is the sum of the horizontal component of acceleration and the gravitational acceleration: 5.0 m/s² + 0 m/s² = 5.0 m/s². The total acceleration in the vertical direction is the difference between the downward component of acceleration and the gravitational acceleration: 3.8 m/s² - 9.8 m/s² = -6.0 m/s².
The force on the rider can be calculated using Newton's second law, which states that force equals mass times acceleration. The mass of the astronaut is 120 kg. The force on the rider in the horizontal direction is given by: force_horizontal = mass × acceleration_horizontal = 120 kg × 5.0 m/s² = 600 N. The force on the rider in the vertical direction is given by: force_vertical = mass × acceleration_vertical = 120 kg × (-6.0 m/s²) = -720 N.
To find the magnitude of the force on the rider by the sled, we can use the Pythagorean theorem. The magnitude of the force is the square root of the sum of the squares of the horizontal and vertical forces: magnitude = sqrt(force_horizontal² + force_vertical²) = sqrt((600 N)² + (-720 N)²) = sqrt(360000 N² + 518400 N²) = sqrt(878400 N²) = 936.33 N (approximately).