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Question: If the soccer player foot makes contact with the ball for T seconds, what is the mag- nitude of the average force vector Favg that her foot exerts on the ball? Write your answer as an expression in terms of the variables: (m, v₁, T, g, h,0)

Question: If the soccer player foot makes contact with the ball for T seconds, what is the mag- nitude of the average force vector Favg that her foot exerts on the ball? Write your answer as an expression in terms of the variables: (m, v₁, T, g, h,0)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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# Problem At the “before” instant shown below, a soccer ball of mass \(m\) is rolling horizontally to the left with speed \(v_1\). A soccer player then kicks the ball as shown in the “after” instant, such that it leaves her foot with speed \(v_2\) making an angle \(\theta\) with the horizontal. The ball just clears her opponent’s head (at height \(h\)) when it reaches the apex of its projectile trajectory. Assume no drag during the projectile motion. The gravitational acceleration is \(g\). **Question:** If the soccer player's foot makes contact with the ball for \(T\) seconds, what is the magnitude of the average force vector \(F_{\text{avg}}\) that her foot exerts on the ball? Write your answer as an expression in terms of the variables: \((m, v_1, T, g, h, \theta)\). ### Explanation of Diagram: - **Before Kick:** - A soccer ball moves horizontally to the left with speed \(v_1\). - The player (indicated in blue) is preparing to kick the ball. - **After Kick:** - The ball is kicked with speed \(v_2\) at an angle \(\theta\). - The projectile motion of the ball is shown, reaching a height \(h\) at its apex. - Gravitational acceleration (\(g\)) acts downward. This visual helps understand how the initial horizontal motion of the ball changes post-kick into a projectile motion, influenced by the angle and force imparted by the player's foot.
Transcribed Image Text:# Problem At the “before” instant shown below, a soccer ball of mass \(m\) is rolling horizontally to the left with speed \(v_1\). A soccer player then kicks the ball as shown in the “after” instant, such that it leaves her foot with speed \(v_2\) making an angle \(\theta\) with the horizontal. The ball just clears her opponent’s head (at height \(h\)) when it reaches the apex of its projectile trajectory. Assume no drag during the projectile motion. The gravitational acceleration is \(g\). **Question:** If the soccer player's foot makes contact with the ball for \(T\) seconds, what is the magnitude of the average force vector \(F_{\text{avg}}\) that her foot exerts on the ball? Write your answer as an expression in terms of the variables: \((m, v_1, T, g, h, \theta)\). ### Explanation of Diagram: - **Before Kick:** - A soccer ball moves horizontally to the left with speed \(v_1\). - The player (indicated in blue) is preparing to kick the ball. - **After Kick:** - The ball is kicked with speed \(v_2\) at an angle \(\theta\). - The projectile motion of the ball is shown, reaching a height \(h\) at its apex. - Gravitational acceleration (\(g\)) acts downward. This visual helps understand how the initial horizontal motion of the ball changes post-kick into a projectile motion, influenced by the angle and force imparted by the player's foot.
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