Science:Math Exam Resources/Courses/MATH110/April 2018/Question 05 (c)
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Question 05 (c) 

A stone is shot vertically into the air at an initial velocity of 16 m/s. Its height (in metres) above the ground after seconds is given by (c) Suppose the same stone is shot vertically on Mars. On Mars the height of the stone above ground after seconds would be
How much higher will the stone travel on Mars than on Earth?

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 

Find the maximum value of the stone heights on Mars and on Earth. For the maximum value on Earth, we can use the part (a). 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By part (a), the maximum of the stone height on Earth occurs at , so the maximum value is Now, we find the maximum value of the stone height on Mars. As we did in part (a), the maximum occurs at satisfying . Since the derivative of the stone height on Mars is
the value is .
Therefore, the maximum on Mars is Finally we get the difference between two maximums as Answer: (metres) 