Science:Math Exam Resources/Courses/MATH110/December 2016/Question 06 (a)

MATH110 December 2016

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Question 06 (a)

Explorers on a small airless planet used a spring gun to launch a small ball vertically upward from the ground at a launch velocity of $15{\text{m}}/{\text{s}}$. The explorers expected the ball to reach a height of $$s(t)=15t-(1/2)gt^{2}$$ metres at $t$ seconds after being launched, where $g$ is a constant. (a) What was the value of $g$ if the ball took $40$ seconds to hit to the ground after the launch?

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
The hit the ground is to have height zero.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. According to the question, we need to solve for ${\textstyle g}$ if ${\textstyle s(40)=0}$. Plugging $t=40$ into the function $s$, $$15\cdot 40-{\dfrac {1}{2}}g\cdot 40^{2}=0\implies 40(15-20g)=0\implies 40\cdot 5(3-4g)=0.$$ Therefore, it is enough to find $g$ satisfying $$3-4g=0,$$ and hence $$g={\dfrac {3}{4}}.$$ Answer: ${\textstyle g={\color {blue}{\dfrac {3}{4}}}.}$