Question

If an object is projected upward with an initial velocity of 123 ft per​ sec, its height h after t seconds is h equals negative 16 t squared plus 123 t. Find the height of the object after 2 seconds.

Answer 1

To find the height of the object after 2 seconds, we can use the given height equation:

\[
h(t) = -16t^2 + 123t
\]

We need to substitute \( t = 2 \) into the equation:

\[
h(2) = -16(2)^2 + 123(2)
\]

Calculating the squared term first:

\[
(2)^2 = 4
\]

Now substitute that back into the equation:

\[
h(2) = -16(4) + 123(2)
\]

Now compute each part:

\[
h(2) = -64 + 246
\]

Now, add the two results:

\[
h(2) = 182
\]

Therefore, the height of the object after 2 seconds is **182 feet**.