Question

A 16300 kg sailboat experiences an eastward force 17300 N due to the tide pushing its hull while the wind pushes the sails with a force of 59000 N directed toward the northwest (45◦ westward of North or 45◦ northward of West). What is the magnitude of the resultant acceleration of the sailboat?

Answer 1

Answer:$2.95 m/s^2$

Explanation:

Given

mass of sailboat 16300 kg

Eastward Force$(F_1)$=17300 N

Northwest Force$(F_2)$=59000

$F_1=17300\hat{i}$

$F_2=-59000cos\hat{i}+59000\hat{j}$

Resultant Force F is given by vector addition of two

$F=F_1+F_2$

$F=17300\hat{i}+-59000cos45\hat{i}+59000sin45\hat{j}$

$F=-24419.30\hat{i}+41719.30\hat{j}$

|F| gives resultant magnitude

$|F|=\sqrt{(24419.30)^2+(414719.30)^2}$

|F|=48340.48 N

therefore acceleration is given by

$a=\frac{F}{m}=\frac{48340.48}{16300}=2.95 m/s^2$