answer the following practice exercises. Practice Exercise 2.2gedA balloon is rising vertically at 4.0 m/s. Wind is blowing from east to west at 3.0 m/s. Find theresultant velocity of the balloon.The parallelogram method may also be used to add more than two vectors. However, the processis tedious. The steps when adding more than two vectors using the parallelogram method are outlinedbelow and demonstrated in Sample Problem 2.3.alAfter drawing the resultant of the first two vectors, construct a second parallelogram using thisresultant and the third vector as sides.1.2.Draw the diagonal of the parallelogram from the common point. This is now the new resultant.3.The process is continued until all vectors have been added.4.The magnitude of the final resultant is determined from the scale used. The direction is measuredby a protractor.Sample Problem 2.3N.A particle is being acted upon by the following forces:F, = 4.0 N, east; F,= 6.0 N, northeast; and F= 8.0 N, south.Find the resultant using the parallelogram method. You may add theforces according to the following grouping (F +F,)+F, .F2R = F, + F,W0 F.R2 = (F, + F) + F,Solution:As shown in the figure, R, = F+F, while R, =R, +F, . Theresultant vector in the figure has nine scale units corresponding to9 N. Using a protractor, the angle that the resultant makes with thehorizontal axis is 25°. Thus, the resultant is 9 N, 25° south of east.F,Y scale: H 1 N Proctice Exercise 2.3Using the same forces in Sample Problem 2.3, find F+(F, +F). Compare your answer with theresultant obtained in Sample Problem 2.3.Polygon MethodThe polygon method is otherwise known as the tip-to-tail method. This method is more convenientthan the parallelogram method when more than two vectors are to be added graphically. The followingare the steps to be followed using the polygon method.1.Represent each vector quantity by an arrow drawn to scale.Starting from the origin, draw the first vector on the rectangular coordinate system, accountingproperly its direction.2.Connect the tail of the second vector to the head of the first vector. Then, connect the tail of thethird vector to the head of the second vector. You may continue drawing the vectors head to tail3.untilyoudraw the last vector to be added.The resultant will close the figure formed by connecting the vectors. This resultant is drawn fromthe tail of the first vector to the head of the last vector.4.5.Measure the length of the arrow representing the resultant. Determine the magnitude of theresultant from the scale used.6.Use a protractor to determine the direction of the resultant.If there are only two vectors toadded, the polygon that will be formed is a triangle. In this case,the polygon method is otherwise known as the triangle method.

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