Question 2 - Projectiles [40 Marks] a) The server now eases off the power and the...

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Question 2 - Projectiles [40 Marks] a) The server now eases off the power and the ball follows a curved projectile under the force of gravity only. Assuming the ball direction leaving the racquet is horizontal to the court surface (i.e. ground), calculate the speed of the ball leaving the racquet if the ball landing position is directly on the corner of the cross court service area line and the singles court sideline, as before. Calculate the ball height above the net cord. Does the ball make it over the net without hitting the net cord? (Marks Breakdown: find struck ball speed [2 marks], height above net [2], does ball hit net [1], workings shown [5]) b) Now assuming the ball leaves the racquet at 154 mph at an angle of 10 degrees below the horizontal, following a curved projectile under the force of gravity only, and assuming the server adjusts the racquet head accordingly without loss of speed, impulse or ball strike position etc., show that the ball landing position is in the vicinity of the corner of the cross court service area line and the singles court sideline, as before. Calculate the ball height above the net cord. Does the ball make it over the net without hitting the net cord? [Assumption: The non-zero initial ball angle trajectory is within the same vertical plane as trajectories from question parts 1b) and 2a)] (Marks Breakdown: find landing distance [1 marks], height above net [1], does ball hit net [1], workings shown [2]) c) To represent the actual projectile of a tennis ball, now consider the effect of drag force in addition to the force due to gravity. Assuming a constant drag coefficient CD of 0.6 for a tennis ball over the course of its flight from a ball strike velocity of 154 mph at an angle of 7 degrees below the horizontal, draw a free body diagram of the forces acting on the ball, find and show that the ball landing position is approximately on the corner of the cross court service area line and the singles court sideline, as before. Calculate the final landing resultant velocity and then calculate the height above the net cord. Does the ball make it over the net without hitting the net cord? Does the ball land inside the service box or is it called out? [Hint: DO NOT USE SUVAT equations, instead refer to the "Non-zero Drag Ballistic Projectiles" lecture notes] [Assumption: The non-zero aerodynamic drag trajectory is within the same vertical plane as trajectories from question parts 1b), 2a) and 2b)] (Marks Breakdown: find landing distance [3 marks], final velocity [3], height above net [3], does ball hit net & land in the service box [3], workings shown [3]) d) Plot the four trajectories (straight line, horizontal initial ball velocity, non-zero initial ball angle & aerodynamic drag case) as described above using a spreadsheet, CAD or otherwise indicating ball height in relation to the net cord. Perhaps zoom in to highlight the different net positions in the plots you include in your report. Comment on the differences between them and offer reasoning as to why they are different, justifying your answer using evidence from your calculations. [around 200-300 words] (Marks Breakdown: plots [5 marks], comments [5]) Question 2 - Projectiles [40 Marks] a) The server now eases off the power and the ball follows a curved projectile under the force of gravity only. Assuming the ball direction leaving the racquet is horizontal to the court surface (i.e. ground), calculate the speed of the ball leaving the racquet if the ball landing position is directly on the corner of the cross court service area line and the singles court sideline, as before. Calculate the ball height above the net cord. Does the ball make it over the net without hitting the net cord? (Marks Breakdown: find struck ball speed [2 marks], height above net [2], does ball hit net [1], workings shown [5]) b) Now assuming the ball leaves the racquet at 154 mph at an angle of 10 degrees below the horizontal, following a curved projectile under the force of gravity only, and assuming the server adjusts the racquet head accordingly without loss of speed, impulse or ball strike position etc., show that the ball landing position is in the vicinity of the corner of the cross court service area line and the singles court sideline, as before. Calculate the ball height above the net cord. Does the ball make it over the net without hitting the net cord? [Assumption: The non-zero initial ball angle trajectory is within the same vertical plane as trajectories from question parts 1b) and 2a)] (Marks Breakdown: find landing distance [1 marks], height above net [1], does ball hit net [1], workings shown [2]) c) To represent the actual projectile of a tennis ball, now consider the effect of drag force in addition to the force due to gravity. Assuming a constant drag coefficient CD of 0.6 for a tennis ball over the course of its flight from a ball strike velocity of 154 mph at an angle of 7 degrees below the horizontal, draw a free body diagram of the forces acting on the ball, find and show that the ball landing position is approximately on the corner of the cross court service area line and the singles court sideline, as before. Calculate the final landing resultant velocity and then calculate the height above the net cord. Does the ball make it over the net without hitting the net cord? Does the ball land inside the service box or is it called out? [Hint: DO NOT USE SUVAT equations, instead refer to the "Non-zero Drag Ballistic Projectiles" lecture notes] [Assumption: The non-zero aerodynamic drag trajectory is within the same vertical plane as trajectories from question parts 1b), 2a) and 2b)] (Marks Breakdown: find landing distance [3 marks], final velocity [3], height above net [3], does ball hit net & land in the service box [3], workings shown [3]) d) Plot the four trajectories (straight line, horizontal initial ball velocity, non-zero initial ball angle & aerodynamic drag case) as described above using a spreadsheet, CAD or otherwise indicating ball height in relation to the net cord. Perhaps zoom in to highlight the different net positions in the plots you include in your report. Comment on the differences between them and offer reasoning as to why they are different, justifying your answer using evidence from your calculations. [around 200-300 words] (Marks Breakdown: plots [5 marks], comments [5])