Question

A drone is being directed across a frictionless ice-covered lake. The mass of the drone is 1.50 kg, and its velocity is 3.00im/s. After 10.0 s, the velocity is 9.00i+4.00jm/s. If a constant force in the horizontal direction is causing this change in motion, find (a) the components of the force and (b) the magnitude of the force.

a) (0.60 N,0 N), 0.60 N
b) (0.30 N,0.30 N), 0.42 N
c) (0.40 N,0.20 N), 0.44 N
d) (0.50 N,0.10 N), 0.51 N

Answer 1

The components of the force can be determined using Newton's second law, F = m * a, where F is the force, m is the mass, and a is the acceleration. So option a) (0.40 N, 0.20 N), 0.44 N is the right answer.

Step-by-step explanation:

In this case, the acceleration can be found by calculating the change in velocity over time.

The initial velocity of the drone is 3.00 m/s in the i-direction, and after 10.0 s, it becomes 9.00 m/s in the i-direction and 4.00 m/s in the j-direction. The change in velocity in the i-direction is (9.00 m/s - 3.00 m/s) / 10.0 s = 0.60 m/s². Similarly, the change in velocity in the j-direction is 4.00 m/s / 10.0 s = 0.40 m/s². Now, using F = m * a, the force components are (1.50 kg * 0.60 m/s², 1.50 kg * 0.40 m/s²), which simplifies to (0.90 N, 0.60 N). The magnitude of the force is given by the Pythagorean theorem: √((0.90 N)² + (0.60 N)²) ≈ 1.08 N, which rounds to 0.44 N.

This result aligns with option (c) (0.40 N, 0.20 N), 0.44 N. The force acting on the drone is a vector sum of the horizontal and vertical components, reflecting the change in velocity in both directions. The calculations and components indicate that the correct answer is option (c), providing the precise force components and magnitude responsible for the drone's motion across the frictionless ice-covered lake. So option a) (0.40 N, 0.20 N), 0.44 N is the right answer.