Question

The engine of a boat (m = 2280 kg) exerts an

1800 N force northward, while the current
pushes it 1050 N eastward.
What is the magnitude of the acceleration
of the boat?

Answer 1

a = 0.9139 [m/s²]

Step-by-step explanation:

To solve this problem we must use Newton's second law, which tells us that the sum of forces on a body is equal to the product of mass by acceleration.

The forces are on two different axes, x & y axes (North and East). In this way, the Pythagorean theorem should be used to determine the total force.

Fx = 1800 [N]

Fy = 1050 [N]

`F = \sqrt{(F_(x) )^(2) +(F_(y) )^(2) } \\F=\sqrt{(1800)^(2) +(1050)^(2) } \\F=2083[N]`

Now using Newton's second law.

ΣF = m*a

where:

F = force = 2083.8 [N] (units of Newtons)

m = mass = 2280 [Kg]

a = acceleration [m/s²]

2083.8 = 2280*a

a = 0.9139 [m/s²]