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Stone launched vertically upward from top of cliff

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1) Luigi launches a stone vertically upward from the top of a cliff. The height of the stone above the base of the cliff is appoximated by the model h=65+10t-5t^2
where t is time in second and h is height in metres

a) how high is the stone above the base of the cliff after 3 seconds?

h = 65 + 10t - 5t^2
h = 65 +10(3) - 5(3)^2
h = 65 +30 - 45
h = 50 m

b) How long does it take for the stone to reach 50m above the base of the cliff?

h = 65 + 10t - 5t^2
h = 65 + 10t - 5t^2
-65 + 50 = 10t - 5t^2
-15 = 10t - 5t^2
can someone help me from here?

c) How long does it take for the stone to hit the ground at the base of the cliff?

I do not know about how to go about completing this one,

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The solution discusses how high the stone above the base of the cliff is.

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Hi, I have started work on these questions but I do not know if I am doing them right, or how to go about the others.
1) Luigi launches a stone vertically upward from the top of a cliff. The height of the stone above the bsae of ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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