Question

A 2 000-kg sailboat experiences an eastward force of 3 000 N by the ocean tide and a wind force against its sails with a magnitude of 6 000 N directed toward the northwest (45 N of W). What is the magnitude of the resultant acceleration? with steps, please.

Answer 1

Answer:

The magnitude of the resultant acceleration is 2.2 $m/s^2$

Explanation:

Mass (m) of the sailboat =  2000 kg

Force acting on the sailboat due to ocean  tide is $F_1$ = 3000N

Eastwards means takes place along the positive x direction

Then$F_{1x}$ = 3000N and $F_{1y}$= 0

Wind Force acting on the Sailboat is$F_2$  = 6000N directed towards the northwest that means at an angle  45 degree above the negative x axis

Then  

$F_{2x}$ = -(6000N) cos 45 degree = -4242.6 N

$F_{2y}$  = (6000N) cos 45 degree = 4242.6 N

Hence  , the net force acting on the sailboat in x direction is  

$F_x = F_{1x}+ F_{2x}$

=  - 3000 N + 4242.6 N

=  - 3000 N +4242.6 N

= 1242.6N

Net Force acting on the sailboat in y direction is  

$F_y = F_{1y}+ F_{2y}$

= 0+ 4242.6N

= 4242.6N

The magnitude of the resultant force =

Using pythagorean theorm of 1243 N and 4243 N

$\sqrt{(1242.6)^2 + (4242.6)^2$

$\sqrt{(1544054.76) + (17999654.8)}$

$\sqrt{(19543709.5)^2}$

4420.8 N

F = ma

$a = \frac{F}{m}$

$a =\frac{4420.8}{ 2000}$

=2.2 $m/s^2$