The engine of a 2280 kg boat exerts a 1800 N force northward, while a current pushes the boat 1050 N eastward.

What is the magnitude of the acceleration of the boat?

[tex]\[ a = [?] \, \text{m/s}^2 \][/tex]



Answer :

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].