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?
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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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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