1. 22 points - The Quasars and the Galaxies are locked up in the Super Duper Bow

Question

1. 22 points - The Quasars and the Galaxies are locked up in the Super Duper Bowl that will determine the Champion of the Universe. Wow, there is a lot riding on this one. Anyway, the Quasars lead by a score of 27 to 26. The Galaxies have the ball but there is only 1.0000000 s left in the game. The ball is on the 31.4000 m line (Universe sports use metric). The Galaxies only hope is a field goal. The ball will have to be kicked from the 38.4000 m line, 7.0000 m behind the line of scrimmage. Fortunately the Galaxies have a rioter named Spike, nicknamed Big Toe, who is extremely accurate and loves physics. He quickly assesses the situation and decides that he should rich the ball from the 38.4000 m line at an angle of 43.5000 degree (taking into account air resistance) at an initial velocity of 20.2938 m/s in order to make the field goal and win the Championship of the Universe. The Crossbar is 3.04800 m high. Use 9.80000 m/s^2 for g. Disregard the size of the football. a. Complete the drawing showing the path of the ball, max height, and range. b. Show with calculations which team is champions of the Universe. In other words is the field goal good? c. What is the total range of the football? d. What is the maximum height the football reaches?

Explanation / Answer

Data given-

Initial velocity, v = 20.2938 m/sec

Co-ordinates of pole = (38.40 I + 3.0480 j)

For horizontal direction-

X = v cos 43.5 *t

38.40 = 20.2938 cos 43.5 *t

t = 2.60 sec

for vertical motion-

Y = v sin 43.5*t

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