Real Life Quadratic Functions How High And Far Can You Hit The Ball When An Athlete Hits A Ball All Of The Following W 1 (43.34 KiB) Viewed 45 times
Real Life Quadratic Functions How High And Far Can You Hit The Ball When An Athlete Hits A Ball All Of The Following W 2 (44.52 KiB) Viewed 45 times
Real Life Quadratic Functions How High And Far Can You Hit The Ball When An Athlete Hits A Ball All Of The Following W 3 (50.3 KiB) Viewed 45 times
Real life quadratic functions: How high and far can you hit the ball? When an athlete hits a ball all of the following would make a difference in the height and distance that the ball goes. +How hard you the ball The angle of the wing • Which way the wind is ning Howard the wind is • Temperature of the air Humidity of the air How high you hit the ball fee ground in the of you is a How the price how the ball - Your device from sea level All of these affect the ball in some way, but in this lab the only ones we will be considering are: 1) How hard you hit the ball. 2) How far off the ground the ball is when you hit it. General quadratic equation: • "h" relates to the height of the ball after some amount of time • "x" relates to the time (normally in seconds) that the ball has traveled • "" relates to earth's gravity with a value of: -16 "relates to the force with which the ball was hit • "e" relates to the height above the ground when the ball was hit • Reminder: When the "a" value is negative the parabola will always be facing downward making the vertex the maximum point. Part 1: Hitting a golf ball into a tower? While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed The formula for this shot is, where he is the height of the ball and x is the number of seconds the ball is in the air A. How could Marc mathematically try to prove that he hit the ball near the top of the tower? B. How high did Marc actually hit the ball? If we consider near the top of the tower to be within in 10 feet of its height is Marc able to mathematically support he hit the ball near the top of the tower?
Part 2: Hitting the green in one shot! Later during that same golf outing Mare decided to show off by trying to hit the green in one shot. He said he hit the green as the ball hung in the air for at least 15 seconds. The formula for this shot is. A. How can Mare provide proof that his shot actually hung in the air for 15 seconds? B. How long did the ball actually hang in the air? Is Marc able to mathematically back up how long he says the ball was in the air? Part 3: Hitting the baseball over the lights Meanwhile at the ballpark Juan was practicing his hitting while talking to some friends. He started telling them how he hit the ball over the 50 foot light tower yesterday. The formula for this hit is, where h is the height of the ball and x is the number of seconds the ball is in the air. A. How can Juan provide proof to the friends that he actually hit the ball over the tower? B. How high did Juan actually hit the ball? Is Juan able to mathematically back up how high he says he hit the ball?
Part 4: Hitting the ball into the parking lot As Juan continued his hitting practice, one of the balls flew over the center field stands and into the parking lot. “Did you see that shot”, he yelled at the friends. "The ball hung in the air for at least 10 seconds”, he exclaimed. The formula for this hit is: where h is the height of the ball and x is the number of seconds the ball is in the air. A. How can Juan provide proof that the ball actually hung in the air for 10 seconds? B. How long did the ball hang actually hang in the air? Is Juan able to mathematically back up how long he says the ball was in the air?
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