25a. You are given a formula for height and told that the value of "r" in the formula is 19.6. You are asked to find the value of t such that h = 14.7. Substitute the given values and solve for t the way you solve any quadratic equation.
14.7 = 19.6t -4.9t²
4.9t² -19.6t +14.7 = 0 . . . . . put the equation in standard form
4.9(t² -4t +3) = 0 . . . . . . . . . factor out 4.9 to simplify the numbers
(t -1)(t -3) = 0 . . . . . . . . . . .. divide by 4.9 and factor
The solutions to this are ...
t = 1, t = 3
After 1 second, the ball will reach the height of 14.7 meters.
25b. This question asks you to find the value of t that make h = 0.
0 = 19.6t -4.9t² . . . . . . substitute the given numbers
0 = 4.9t(4 -t) . . . . . . . . factor
The solutions to this are ...
t = 0, t = 4
The ball will hit the ground after 4 seconds.
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As you can see from the graph below, a graphing calculator can be helpful for solving problems of this sort.