Question

Two small forces, →F1=−2.40ˆi−6.10ˆj N and →F2=8.50ˆi−9.70ˆj N, are exerted on a rogue asteroid by a pair of space tractors.

(a) Find the net force.
(a) -10.9ˆi+3.6ˆj N, (b) 11.7 N at 17° below the x-axis, (c) -0.087ˆi+0.29ˆj m/s², (d) 0.30 m/s² at 73° above the x-axis

Answer 1

This Physics question for the High School grade, focuses on finding the net force and acceleration of an asteroid acted upon by two forces. The net force is 6.10î - 15.80ĵ N. The magnitude of the net force is 10.9 N at 66.4° below the x-axis. Option b is the correct answer.

Step-by-step explanation:

To find the net force, we need to add the two given forces. Adding the x-components of the forces gives us -2.40 N + 8.50 N = 6.10 N. Adding the y-components of the forces gives us -6.10 N - 9.70 N = -15.80 N. Therefore, the net force is 6.10î - 15.80ĵ N.

To find the magnitude and direction of the net force, we can use Pythagorean's theorem. The magnitude of the net force is given by √((6.10 N)² + (-15.80 N)²) = √(37.21 N² + 249.28 N²) = 10.9 N. The direction of the net force can be found by taking the angle θ = atan((-15.80 N)/(6.10 N)) = -66.4° below the x-axis.

Therefore, the correct answer is (b) 10.9 N at 66.4° below the x-axis.