Question

a horse gallops 6 miles west, and then turns 10° north of west and gallops 7 more miles. what is the direction of the horses resultant vector? measure the angle from the positive x - axis. |\overrightarrow{r}| = 12.95 miles \theta = ?^\circ

Explanation:

Step1: Analyze the components of each displacement

The first displacement is 6 miles west, so its x - component (\(x_1\)) is \(- 6\) miles (negative because west is in the negative x - direction) and its y - component (\(y_1\)) is \(0\) miles.

The second displacement is 7 miles at an angle of \(10^{\circ}\) north of west. The angle of this displacement with respect to the negative x - axis is \(10^{\circ}\). So, the x - component of the second displacement (\(x_2\)) is \(-7\cos(10^{\circ})\) and the y - component (\(y_2\)) is \(7\sin(10^{\circ})\).

Step2: Calculate the total x - component (\(R_x\)) and total[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]

Answer:

Step1: Analyze the components of each displacement

The first displacement is 6 miles west, so its x - component (\(x_1\)) is \(- 6\) miles (negative because west is in the negative x - direction) and its y - component (\(y_1\)) is \(0\) miles.

The second displacement is 7 miles at an angle of \(10^{\circ}\) north of west. The angle of this displacement with respect to the negative x - axis is \(10^{\circ}\). So, the x - component of the second displacement (\(x_2\)) is \(-7\cos(10^{\circ})\) and the y - component (\(y_2\)) is \(7\sin(10^{\circ})\).

Step2: Calculate the total x - component (\(R_x\)) and total[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]