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Answer :
Final answer:
The times when the toy rocket is at a height of 100 feet are 3.79 seconds and 0.54 seconds, found by solving the quadratic equation formed by setting the rocket's height equation equal to 100.
Explanation:
To solve for the time(s) when the toy rocket will be 100 ft from the ground, we need to set the equation s(t) = -16t2 + 96t equal to 100 feet and solve for t. The equation becomes:
-16t2 + 96t - 100 = 0
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, applying the quadratic formula is the most straightforward method:
t = (-b ± sqrt(b2 - 4ac)) / (2a)
Where a = -16, b = 96, and c = -100. After substituting the values and simplifying, we get two solutions for t:
- t = 3.79 s (the time when the rocket is coming down)
- t = 0.54 s (the time when the rocket is going up)
Both times are when the rocket is at the height of 100 feet above the ground, once on the way up and once on the way down.
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