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Answer :
Final answer:
The toy rocket, modeled by the equation h=−4.9t²+23.8t+3.5, will hit the ground approximately 3.79 seconds after it is launched.
Explanation:
The time it will take for the toy rocket to hit the ground can be determined using the given quadratic equation, which models the height of the rocket in relation to time. In this scenario, the height (h) becomes zero when the rocket hits the ground. So, the equation is set to zero and solved for 't' using the quadratic formula:
h=−4.9t²+23.8t+3.5 = 0
The quadratic formula gives two solutions, which represent two distinct points in time. However, in this case, we're interested in the later time (when the rocket falls back to the ground after reaching its peak), so we consider the larger value. Using the quadratic formula yields two solutions: t = 3.79 s and t = 0.54 s. Since we're interested in when the rocket hits the ground, we take the larger value:
t = 3.79 s.
This implies that the toy rocket will hit the ground approximately 3.79 seconds after it has been launched.
Learn more about quadratic formula here:
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