SOLUTION: For a water balloon launched from a 49-meter overlook with an initial vertical velocity of 24.5 meters per second, the height h in meters as a function of time t in seconds is h=âˆ
Question 1184127: For a water balloon launched from a 49-meter overlook with an initial vertical velocity of 24.5 meters per second, the height h in meters as a function of time t in seconds is h=−4.9t^2+24.5t+49. When will the balloon land and burst? Answer by ikleyn(52778) (Show Source):
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For a water balloon launched from a 49-meter overlook with an initial vertical velocity of 24.5 meters per second,
the height h in meters as a function of time t in seconds is h=−4.9t^2+24.5t+49. When will the balloon land and burst?
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To answer the question, you should solve this equation
h(t) = 0, which is -4.9t^2 + 24.5t + 49 = 0.
Divide the left side by -4.9. You will get much more pleasant EQUIVALENT equation
t^2 - 5t - 100 = 0.
Use the quadratic formula to find its roots
= = .
Choose the positive root (and deny negative one)
t = = 12.81.
ANSWER. The event will happen in 12.81 seconds.
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