Certainly! Let's solve this problem step by step:
1. Identify the Forces: We have two forces acting on the boat:
- A force of 1800 N directed northward.
- A force of 1050 N directed eastward.
2. Calculate the Magnitude of the Net Force: Since these forces are perpendicular to each other, we can use the Pythagorean theorem to find the resultant force (net force):
[tex]\[
F_{\text{net}} = \sqrt{F_{\text{northward}}^2 + F_{\text{eastward}}^2}
\][/tex]
Substituting the given values:
[tex]\[
F_{\text{net}} = \sqrt{1800^2 + 1050^2} \approx 2083.87 \, \text{N}
\][/tex]
3. Applying Newton's Second Law: To find the acceleration of the boat, we use Newton's second law of motion, which states:
[tex]\[
F = ma
\][/tex]
Rearranging for acceleration [tex]\(a\)[/tex]:
[tex]\[
a = \frac{F_{\text{net}}}{m}
\][/tex]
Given that the mass [tex]\(m\)[/tex] of the boat is 2280 kg, we substitute the values:
[tex]\[
a = \frac{2083.87}{2280} \approx 0.914 \, \text{m/s}^2
\][/tex]
So, the magnitude of the acceleration of the boat is approximately [tex]\(0.914 \, \text{m/s}^2\)[/tex].
