SAT Mathematics Practice Test 3

Question : 33 of 58

Marks: +1, -0

h=-16t^2+vt+k

The equation above gives the height h, in feet, of aball 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

$v=h+k-16k$
$v={h-k+16}/t$
$v={h+k}/t-16t$
$v={h-k}/t+16t$

Validate

Solution:

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={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={h-k}/t+{16t^2}/t

, which can be simplified to

v={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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