a. To determine The velocity vector and position vector, for t ≥ 0 . Explanation Given: A baseball with an initial poition of 〈 x 0 , y 0 〉 = 〈 0 , 3 〉 hit at an angle of 60 ° with an initial speed of 80ft/s. Definition used: Let the position vector of an object moving in two dimensional space be given by r ( t ) = 〈 x ( t ) , y ( t ) 〉 for t ≥ 0 . Then, the velocity of the object v ( t ) is the derivative of the position vector, r ′ ( t ) = 〈 x ′ ( t ) , y ′ ( t ) 〉 . The acceleration of the objects is the derivative of the velocity of the object a ( t ) = v ′ ( t ) . Then, velocity can be obtained from antiderivative of acceleration vector as v ( t ) = ∫ ( a ( t ) ) d t and the position vector can be obtained from antiderivative of velocity vector as r ( t ) = ∫ v ( t ) d t . Calculation: Here the gravitational force acts on the ground (downwards). Thus, the acceleration vector on the object is a ( t ) = 〈 0 , − 32 〉 where the gravitational of earth is 32 ft/s 2 . Given initial speed 80ft/s at 60 ° . Let v ( t ) = 〈 v x ( t ) , v y ( t ) 〉 at t = 0. Obtain the value of 〈 u 0 , v 0 〉 at t = 0 as follows, 〈 u 0 , v 0 〉 = 〈 80 cos 60 ° , 80 sin 60 ° 〉 = 〈 80 1 2 , 80 3 2 〉 = 〈 40 , 40 3 〉 ft/s The acceleration is a ( t ) = 〈 0 , − g 〉 , 〈 u 0 , v 0 〉 is 〈 40 , 40 3 〉 ft/s and initial position 〈 x 0 , y 0 〉 is 〈 0 , 3 〉 b. To determine The time of flight and the range of the object. c. To determine The maximum height of the object.

3rd Edition

ISBN: 9780135962138

Author: Briggs

Publisher: PEARSON CO

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Chapter 14, Problem 35RE

To determine

The velocity vector and position vector, for t≥0.

To determine

The time of flight and the range of the object.

To determine

The maximum height of the object.

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Chapter 14 Solutions

EP CALCULUS:EARLY TRANS.-MYLABMATH 18 W

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