Question

A boat has a mass of 4900 kg. Its engines generate a drive force of 4600 N due west, while the wind exerts a force of 670 N due east and the water exerts a resistive force of 1170 N due east. Take west to be the positive direction. What is the boat's acceleration, with correct sign?

Answer 1

a = +0.56 m/s² (due west)

Step-by-step explanation:

We apply Newton's second law:

∑Fx = m*a (Formula 1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Data:

m= 4900 kg

Fd= 4600 N : drive force

Fw = 670 N : wind force

Fr = 1170 N : water resistive force

Problem development

We apply the formula (1)

∑Fx = m*a

Fd-Fw-Fr = m*a

4600 - 670 - 1170 = 4900 *a

2760 = 4900 *a

a= (2760) / ( 4900 )

a = +0.56 m/s² (due west)