Explanation Given: A soccer ball was kicked from the ground level with ( x , y ) - coordinates ( 85 , 20 ) on the soccer field shown in figure 1, and with initial velocity v 0 = 10 i − 5 j + 25 k ft/s . The goal net has the height 8 ft and width 24 ft. The acceleration due to gravity is 32 ft/s 2 . Calculation: Let the position vector of the ball when it was hit be r ( t ) . Then, r ( t ) = 〈 85 , 20 , 0 〉 . The velocity vector is given as: v ( t ) = ∫ a ( t ) d t = 〈 0 , 0 , − 32 t 〉 + C 0 . ......... (1) The ball was launched with speed of v 0 = 10 i − 5 j + 25 k ft/s . From (1), v ( 0 ) = 〈 0 , 0 , − 32 ⋅ 0 〉 + C 0 〈 10 , − 5 , 25 〉 = 〈 0 , 0 , 0 〉 + C 0 C 0 = 〈 10 , − 5 , 25 〉 Therefore, the equation (1) becomes, v ( t ) = 〈 0 , − 32 t 〉 + 〈 10 , − 5 , 25 〉

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ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 13.5, Problem 26E

To determine

(a)

The position function that gives the position of the ball t seconds after when it was a hit.

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Chapter 13.5, Problem 25E

Chapter 13.5, Problem 27E

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Brazilian soccer star Marta has a penalty kick in the quarter-final match. She kicks the soccer ball from ground level with the (x, y)-coordinates (76, 21) on the soccer field shown in the figure and with initial velocity vo = 8i - 4j+23k ft/s. Assume an acceleration of 32 ft/s² due to gravity and that the goal net has a height of 8 ft and a total width of 24 ft. 105 ft 1 105 ft r₁ = rj = rk = 165 ft Determine the position function that gives the position of the ball t seconds after it is hit. (Use symbolic notation and fractions where needed.) r(t) = ri(t)i + rj(t)j + rk(t)k Incorrect 81+76 -41+21 ↓ 23r+1672² 165 ft 12 12

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(a) The position function that gives the position of the ball t seconds after when it was a hit.

Solution Summary: The author explains the position function that gives the ball's position t seconds after it was a hit.