Problem 4.6 A sailboat is traveling east at 4.4 rn/s . A sudden gust of wind giv

Question

Problem 4.6 A sailboat is traveling east at 4.4 rn/s . A sudden gust of wind gives the boat an acceleration a = (0.80 n/s^2m , 40 degree north of east). Part A What is the boat^?s speed 4.6 s later when the gust subsides? Express your answer using the appropriate number of significant figures and include the appropriate units. Part B What is the boat^?s direction 4.6 s later when the gust subsides? Express your answer using the appropriate number of significant figures and include the appropriate units.

Explanation / Answer

Here .

initial speed of boat , u = 4.4 i m/s

a = (0.80 * cos(40) , 0.80 * sin(40)) m/s^2

a = (0.613 , 0.514 ) m/s^2

a = 0.613 i + 0.514 j m/s^2

part A) using first equation of motion

v = u + a*t

v = 4.4 i + 4.6 ( 0.613 i + 0.514 j )

v = 7.22 i + 2.36 j m/s

speed = sqrt(7.22^2 + 2.36^2)

speed = 7.6 m/s

the speed of boat is 7.6 m/s

part B)

direction = arctan(2.36/7.22)

direction = 18.1 degree

the direction of motion is 18.1 degree north of east

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