To determine The resultant velocity and acceleration of the golf ball for t = 6.0 s . Explanation Procedure used: 1. To find the velocity of an object whose coordinates are given in parametric form: Step 1: Determine the x – component of velocity v x by finding the derivative d x d t . Step 2: Determine the y – component of velocity v y by finding the derivative d y d t . Step 3: Compute the resultant velocity by using the formula, v = v x 2 + v y 2 and the direction of the moving object by the formula, tan θ = v y v x . 2. To find the acceleration of an object whose coordinates are given in parametric form: Step 1: Determine the x – component of acceleration a x by finding the derivative d v x d t where v x is the x – component of velocity. Step 2: Determine the y – component of acceleration a y by finding the derivative d v y d t where v y is the y – component of velocity. Step 3: Compute the magnitude of acceleration by using the formula, a = a x 2 + a y 2 and the direction of acceleration by the formula, tan θ = a y a x . Calculation: Given that the equations x = 25 t and y = 36 t − 4.9 t 2 ( x and y in meters , t in seconds ) , which describes the motion of a golf ball. Obtain the x – component of velocity by computing the derivative, d x d t as shown below. v x = d x d t = d d t ( 25 t ) = 25 t 1 − 1 ( Since d u n d x = n u n − 1 d u d x ) = 25 For t = 6.0 s , the x – component of velocity becomes, v x | t = 6 = 25 Obtain the y – component of velocity by computing the derivative, d y d t as shown below. v y = d y d t = d d t ( 36 t − 4.9 t 2 ) = 36 t 0 − 4.9 ( 2 ) t 2 − 1 ( Since d u n d x = n u n − 1 d u d x ) = 36 − 9.8 t For t = 6.0 s , the y – component of velocity becomes, v y | t = 6 = 36 − 9.8 ( 6 ) = 36 − 58.8 = − 22.8 The magnitude of the velocity is computed as follows. v = v x 2 + v y 2 = ( 25 ) 2 + ( − 22.8 ) 2 = 625 + 519

11th Edition

ISBN: 9780134508290

Author: Evans

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 24.3, Problem 17E

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The resultant velocity and acceleration of the golf ball for t=6.0s.

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Chapter 24.3, Problem 16E

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EBK BASIC TECHNICAL MATHEMATICS

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