Question

Two ants at a picnic find a small piece of cake. Each picks up the cake and tries to carry it home. The first ant's home is due west, and he pulls with a force of 5.0 N. The second ant's home is due south, and he pulls with a force of 7.0 N. Which of the following is the correct answer for the direction the cake ends up going?

a. Northeast.
b. Northwest.
c. Southeast.
d. Southwest.

Answer 1

The cake ends up going in the southeast direction.

Step-by-step explanation:

The first ant is pulling west with a force of 5.0 N, and the second ant is pulling south with a force of 7.0 N. To determine the direction the cake ends up going, we can use vector addition. We can represent the force exerted by the first ant as a vector pointing west and the force exerted by the second ant as a vector pointing south. When we add these two vectors, the resulting vector will represent the direction the cake ends up going.

To add these vectors, we can use the Pythagorean theorem and trigonometry. The magnitude of the resultant vector can be found using the equation: magnitude = sqrt((5.0 N)^2 + (7.0 N)^2). The angle of the resultant vector can be found using the equation: angle = arctan(7.0 N / 5.0 N). When we plug in the values, we find that the magnitude of the resultant vector is approximately 8.6 N and the angle is approximately 53 degrees. Therefore, the cake ends up going in the southeast direction. Therefore, the correct answer is c. Southeast.