A model sailboat is slowly sailing west across a pond at 0.342 m/s. A gust of wind blowing at 28.7° south of west gives the sailboat a constant acceleration of magnitude 0.305 m/s2 during a time interval of 1.87 s. If the net force on the sailboat during the 1.87-s interval has magnitude 0.316 N, what is the sailboat's mass?

Question

A model sailboat is slowly sailing west across a pond at 0.342 m/s. A gust of wind blowing at 28.7° south of west gives the sailboat a constant acceleration of magnitude 0.305 m/s2 during a time interval of 1.87 s. If the net force on the sailboat during the 1.87-s interval has magnitude 0.316 N, what is the sailboat's mass? 
What is the new velocity of the boat after the 1.87 s gust of wind? 
And what is the new direction of the boat after the 1.87 s gust of wind?

Steve · Answer

the only unbalanced force is the gust. That is , the steady wind driving the boat west provides no acceleration, so can be disregarded.

F = ma
.316 = m*.305
m = 1.036kg

during the gust, v is increased by a*t = 1.87*.305 = 0.570 = -.569i - .274j
final v = -.911i - .274j
|v| = .951

tanθ = -.274/-.911 = .300
θ = 16.7°, so W16.7°S