Question

The accelerating force of the wind on a small 200-kg sailboat is 707 N north. If the drag of the keel is 500 N acting west, what is the acceleration of the boat?
A) 1.5 m/s2 35 degrees north of east
B) 2.5 m/s2 55 degrees north of west
C) 3.0 m/s2 35 degrees north of east
D) 4.3 m/s2 55 degrees north of west
E) 1.5 m/s2 55 degrees north of west

Answer 1

To determine the acceleration of the boat, we first need to find the net force acting on the boat. We can do this by using the Pythagorean theorem to find the magnitude of the net force and inverse tangent to find the direction.

First, let's find the magnitude of the net force.

F_net = sqrt(F_wind^2 + F_drag^2) = sqrt(707^2 + 500^2) = 867 N

Next, let's find the direction. We can do this by finding the angle θ between the net force and the east direction using inverse tangent (arctan).

θ = arctan(F_wind / F_drag) = arctan(707 / 500) = 54.7 degrees

Finally, we can find the acceleration by dividing the net force by the mass of the boat.

a = F_net / m = 867 N / 200 kg = 4.335 m/s^2

Therefore, the acceleration of the boat is approximately 4.3 m/s^2, 55 degrees north of west, which is option D.