0 0.02 0.04 0.06 0.079996 0.099996 0.119996 0.139996 0.159999 0.179995 0.199989
ID: 3277269 • Letter: 0
Question
0
0.02
0.04
0.06
0.079996
0.099996
0.119996
0.139996
0.159999
0.179995
0.199989
0.219979
0.239969
0.259969
0.279959
0.299959
0.319949
0.339949
0.359949
0.379939
0.399939
0.419939
0.439939
0.459929
0.479919
0.499919
0.519919
0.539909
0.559899
0.579889
0.599879
0.619869
0.639869
0.659869
0.679869
0.09003
0.29529
0.48974
0.6698
0.83905
0.99749
1.14154
1.27118
1.39001
1.49444
1.59527
1.67809
1.74291
1.80053
1.84374
1.86895
1.89056
1.89056
1.88336
1.86175
1.82934
1.78253
1.72491
1.64569
1.56286
1.46563
1.3504
1.23156
1.09832
0.95068
0.78503
0.61218
0.42493
0.22327
0
Question 1: Enter the data from the table into the lists on your calculator (for a little less accurate answer, you can enter every other data point if you wish). Use the quadratic regression feature on your calculator to find the equation of the best fit parabola for the height of the ball, h(t).
Equation:_________________________________
For a good check, do a STAT PLOT of the data points and then graph the regression equation on top of your data to make sure it really is a good fit.
C. Using the Equation
Question 2: What are the units for t and h(t)?
Question 3: If I write h(0.5) = 1.5, what would that be telling me?
Question 4: Even though it isn’t in the table, how could you determine how high the ball is at exactly time t = 0.4 seconds? Go ahead and do it and tell me the height.
Question 5: If I wanted to know the time when the ball was at a height of 1 foot, how would I do that? Go ahead and do it and tell me the time(s).
Question 6: Find an equation that would give the instantaneous velocity at any time t.
Question 7: What would the units of h / (t) be?
Question 8: If your equation gave h / (0.1) = 0.2 , what would that mean?
Question 9: Determine the velocity of the ball at time t = 0.2 seconds.
Question 10: Determine when the velocity of the ball was 10 ft/s.
Question 11: At what point on the path of the ball is the velocity zero?
Question 12: What does it mean for a velocity to be negative?
Question 13: Use your velocity equation to determine (algebraically) at what time the ball reaches the maximum height.
Question 14: Use the answer from question 13 and algebraically determine how high the ball went.
Question 15: Acceleration is the rate of change of velocity with respect to time. Therefore, acceleration can be found by differentiating velocity. What is the acceleration equation in this problem? (Your answer tells you the acceleration due to Earth's gravity.)
Question 16: When did the ball hit the ground?
Question 17: With what velocity did the ball hit the ground when it came back down?
Question 18: What would the velocity equation be for a ball that had a height equation of h(t) = -16t2 + 45t + 4?
Question 19: What would the acceleration equation be for a spaceship traveling with a height function of h(t) = 13t3 – t2 + 40t + 50?
0
0.02
0.04
0.06
0.079996
0.099996
0.119996
0.139996
0.159999
0.179995
0.199989
0.219979
0.239969
0.259969
0.279959
0.299959
0.319949
0.339949
0.359949
0.379939
0.399939
0.419939
0.439939
0.459929
0.479919
0.499919
0.519919
0.539909
0.559899
0.579889
0.599879
0.619869
0.639869
0.659869
0.679869
0.09003
0.29529
0.48974
0.6698
0.83905
0.99749
1.14154
1.27118
1.39001
1.49444
1.59527
1.67809
1.74291
1.80053
1.84374
1.86895
1.89056
1.89056
1.88336
1.86175
1.82934
1.78253
1.72491
1.64569
1.56286
1.46563
1.3504
1.23156
1.09832
0.95068
0.78503
0.61218
0.42493
0.22327
0
Explanation / Answer
1)
h = 0.08405191 + 10.743599*t -15.96728 *t^2
Question 2: What are the units for t and h(t)?
t - sec , h- feet
Question 3: If I write h(0.5) = 1.5, what would that be telling me?
using predicted equation
h(0.5) =
Question 4: Even though it isn’t in the table, how could you determine how high the ball is at exactly time t = 0.4 seconds? Go ahead and do it and tell me the height.
at t = 0.4
h =
Question 5: If I wanted to know the time when the ball was at a height of 1 foot, how would I do that? Go ahead and do it and tell me the time(s).
h(t) = 1
solving we get
t = 0.1 and t = 0.57 approx
Question 6: Find an equation that would give the instantaneous velocity at any time t.
v = dh/dt = 10.743599 -2*15.96728 *t
Post rest question again
You can upload result of regression , so that other don't have to do calculation again
Please rate
t h 0 0.09003 0.02 0.29529 0.04 0.48974 0.06 0.6698 0.08 0.83905 0.1 0.99749 0.12 1.14154 0.14 1.27118 0.16 1.39001 0.18 1.49444 0.2 1.59527 0.22 1.67809 0.24 1.74291 0.26 1.80053 0.28 1.84374 0.3 1.86895 0.32 1.89056 0.34 1.89056 0.36 1.88336 0.38 1.86175 0.4 1.82934 0.42 1.78253 0.44 1.72491 0.46 1.64569 0.48 1.56286 0.5 1.46563 0.52 1.3504 0.54 1.23156 0.56 1.09832 0.58 0.95068 0.6 0.78503 0.62 0.61218 0.64 0.42493 0.66 0.22327 0.68 0Related Questions
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