FC: Elena Olson Question 8
1: 8.) Australia's Olympic athlete Jane Fleming completed in the heptathlon. One of the events was shot-put. It is known that she released the shot about 2 meters above the ground at a speed of about 14 meters per second and at an angle of 45 degrees to the horizontal. With this information, scientists calculate that the height above the ground, y meters, of Jane's shot is given by the rule: y=-0.05x^2 +x + 2 , where x is the horizontal distance the shot has traveled in meters. 1.) How high is the shot after it has traveled 6 meters horizontally from where Jane Fleming released it? 2.) How high is the shot after it has traveled 14 meters horizontally from where Jane Fleming released it? 3.) Find the highest point reached by the shot in its flight. 4.) Find how far from Jane the shot will land.
2: 1.) How high is the shot after it has traveled 6 meters horizontally from where Jane Fleming released it? When I put the rule that the scientists came up with into my calculator, it showed me that after it had traveled 6 meters from where Jane shot it, it was at 6.8 meters high. Since Jane released it 2 meters above the ground, when I went to my table to see how high the shot would be, I counted 2 as 0. So when I got to 8 I knew I was at 6 meters and in the y column it showed me that it was 6.8 meters high at 6 meters.
3: 2.) How high is the shot after it has traveled 14 meters horizontally from where Jane Fleming released it? According the graph on my calculator, it shows that after Jane has thrown it and it has traveled 14 meters the shot-put is on it's way down and is at a height of 5.2 meters. When I went to my table again, I started counting at 2 instead of 0 because Jane let the shot put go at 2 meters. When I got to 16, I knew that it was 14 meters. In the y column next to 16 it stated that the shot put as at 5.2 meters in the air.
4: 3.) Find the highest point reached by the shot in its flight. The highest point that the shot has gone is 6.99 meters. To find the highest point that the shot-put went to I went to 'TRACE' on my calculator, and moved the cursor to around the area of the top of the parabola. Then I hit, 2nd 'TRACE' and chose 'maximum' and hit 'ENTER' 3 times. The calculator came out with the number 6.99.
5: 4.) Find how far from Jane the shot will land. The shot will land about 21.28 meters away from Jane after she shot it. To find out how far away it will be from Jane, I hit 'TRACE' on my calculator and moved the cursor over to where the parabola met the x-axis for the second time. Then I hit 2nd 'TRACE', 'intersect', and hit enter 3 times to find where the parabola met the x-axis, and the number showed up as 21.28 meters.