## Que: A ball thrown up in the air is at a height of h feet, t seconds after it was thrown, where.....

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### Que: A ball thrown up in the air is at a height of h feet, t seconds after it was thrown, where.....

by [email protected] Revolution » Mon Jun 14, 2021 10:58 pm

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Que: A ball thrown up in the air is at a height of h feet, t seconds after it was thrown, where $$h=\ -5\left(t-20\right)^2+180$$. What is the height of the ball once it reached its maximum height and then descended for 5 seconds?

A) 55 feet
B) 105 feet
C) 190 feet
D) 200 feet
E) 255 feet Math Revolution

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[Course] Starting $79 for on-demand and$60 for tutoring per hour and $390 only for Live Online. Email to : [email protected] Elite Legendary Member Posts: 3950 Joined: 24 Jul 2015 Location: Las Vegas, USA Thanked: 19 times Followed by:36 members ### Re: Que: A ball thrown up in the air is at a height of h feet, t seconds after it was thrown, where..... by [email protected] Revolution » Wed Jun 16, 2021 7:54 pm Solution: We know that $$h=-5\left(t - 20\right)^2+180$$. We will first find the value for ‘t’ for which ‘h’ will be maximum. For ‘h’ to be maximum, $$-5\left(t-20\right)^2$$ should be maximum. Since $$-5\left(t-20\right)^2$$ is a perfect square, therefore, $$-5\left(t-20\right)^2$$ ≥ 0. But, $$-5\left(t-20\right)^2$$ will be ≤ 0 [By the property of reverse inequality] So, for ‘h’ to be maximum $$-5\left(t-20\right)^2$$ = 0 => $$-5\left(t-20\right)^2$$ => $$\left(t-20\right)^2$$ => (t − 20) = 0 => t = 20. ‘5’ seconds after ball has reached maximum height ‘h’ at t = 20 + 5 = 25. => $$h=-5\left(25-20\right)^2+180$$ => $$h=-5\left(5\right)^2+180$$ => h = −5 * 25 + 180 => h = -125 + 180 => h = 55 feet A is the correct answer. Answer A Math Revolution The World's Most "Complete" GMAT Math Course! Score an excellent Q49-51 just like 70% of our students. [Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions. [Course] Starting$79 for on-demand and $60 for tutoring per hour and$390 only for Live Online.
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