Question A sailboat is traveling east at 3.4 m/s . A sudden gust of wind gives t

Question

Question

A sailboat is traveling east at 3.4 m/s . A sudden gust of wind gives the boat an acceleration a  = (0.80 m/s2, 40 north of east).

a. What is the boat's speed 5.9 s later when the gust subsides?

Express your answer using the appropriate number of significant figures and include the appropriate units.

b. What is the boat's direction 5.9 s later when the gust subsides?

Express your answer using the appropriate number of significant figures and include the appropriate units.

(This is the second time I posted this qeustion because the last person had both parts incorrect) Part a is not 7.02 and part b is not 22

Explanation / Answer

(a)
Velocity of boat , Vb = 3.4 i^ m/s
Aceleration, a = 0.80 m/s^2   @ 40 north of east
a = 0.8 * cos(40) i^ + 0.8 * sin(40) j^ m/s^2
a = 0.61i^ + 0.51 j^ m/s^2

ux = 3.4 m/s
ax = 0.61 m/s^2

Vx = ux + ax * t
Vx = 3.4 + 0.61 * 5.9
Vx = 7.0 m/s

uy = 0
ay = 0.51 m/s^2

Vy = uy + ay *t
Vy = 0 + 0.51 * 5.9
Vy = 3.0 m/s

Final Velocity, V = sqrt(Vx^2 + Vy^2)
V = sqrt(7.0^2 + 3.0^2)
V = 7.6 m/s

Speed of boat, Vb = 7.6 m/s

(b)
Direction = tan^-1(3.0/7.0)
Direction = 23.2o North of east

I hope you are satisfied with this answer, if not please let me know :)

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