A boat has a mass of 7660 kg. Its engines generate a drive force of 4080 N due west, while the wind exerts a force of 680 N due east and the water exerts a resistive force of 1160 N due east. Take west to be the positive direction. What is the boat's acceleration, with correct sign

0.29 m/s due west.

Explanation:

According to newton's second law,

Net force acting on an object = mass*acceleration

From the question,

F+F₁+F₂ = ma ... Equation 1

Where F = The force generated from the engine, F₁ = Force exerted by the wind, F₂ = Force exerted due to the water, m = mass of the boat, a = acceleration of the boat.

Given: F = 4080 N, F₁ = - 680 N (east), F₂ = - 1160 N (east). m = 7660 kg

substitute into equation 1

4080-680-1160 = 7660 (a)

2240 = 7660a

Therefore,

a = 2440/7660

a = 0.29 m/s due west.