Answer:
A. 39 m
B. approximately t = 1.756 seconds
C. maybe; it depends on the design of the ride (and the accuracy of the model)
Step-by-step explanation:
Part A:
The "starting" value is generally understood to be the value when t=0. Here, we have ...
h(0) = -9.8·0² -5·0 +39 = 0 +0 +39 = 39
The starting height is 39 meters.
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Part B:
The height of the riders will be 0 for the value of t that makes h(t) = 0. That is the solution to the equation ...
-9.8t² -5t +39 = 0
Using the quadratic formula, the solution for ax²+bx+c = 0 is ...
x = (-b±√(b²-4ac))/(2a) . . . . . . . we have a=-9.8, b=-5, c=39
Then the time can be found to be ...
t = (-(-5)±√((-5)²-4(-9.8)(39)))/(2(-9.8)) = (-5±√1553.8)/19.6
t ≈ (-5 ± 39.4183)/19.6 ≈ {-2.266, +1.756}
Only the positive solution is of interest, so ...
t ≈ 1.756 . . . seconds
The height of the riders will equal 0 about 1.756 seconds after the start of the ride.
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Part C:
To the extent that the given function accurately models the height of a rider, there does exist a time at which the rider's height is actually zero. There may be any of a number of reasons why the rider's height may not be zero:
- the model is not completely accurate for values of h(t) near 0. (The ride design may have a minimum positive height, for example.)
- the domain of the function does not include the time when the rider's height is zero
