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h = −16t\(^2\) + vt + kThe equation above gives the height h, in feet, of a ba...


Question

h = −16t\(^2\) + vt + k

The equation above gives the height h, in feet, of a ball t seconds after it is thrown straight up with an initial speed of v feet per second from a height of k feet. Which of the following gives v in terms of h, t, and k ?

Options

A)
v = h + k - 16t
B)
v = \(\frac{h - k + 16}{t}\)
C)
v = \(\frac{h + k}{t}\) - 16t
D)
v = \(\frac{h - k}{t}\) + 16t

The correct answer is D.

Explanation:

Choice D is correct. Starting with the original equation, h = -16t\(^2\) + vt + k, in order to get v in terms of the other variables, -16t\(^2\) and k need to be subtracted from each side. This yields vt = h + 16t\(^2\) - k, which when divided by t will give v in terms of the other variables. However, the equation v = \(\frac{h + 16t^2 - k}{t}\)is not one of the options, so the right side needs to be further simplified. Another way to write the previous  equation is v = \(\frac{h - k}{t} + \frac{16t^2}{t}\), which can be simplified to v = \(\frac{h - k}{t}\) + 16t.

Choices A, B, and C are incorrect and may be the result of arithmetic errors when rewriting the original equation to express v in terms of h, t, and k.


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