Question

1. a 675 n object is pulled horizontally by a force of 410 n as shown. what is the angle between the rope and the vertical?

Explanation:

Step1: Identify the tangent - function relationship

We know that $\tan\theta=\frac{F_{horizontal}}{F_{vertical}}$. Here, $F_{horizontal} = 410\ N$ and $F_{vertical}=675\ N$.

Step2: Calculate the tangent of the angle

$\tan\theta=\frac{410}{675}\approx0.6074$.

Step3: Find the angle

$\theta=\arctan(0.6074)$. Using a calculator, $\theta\approx31.3^{\circ}$.

Answer:

$31.3^{\circ}$