Question

Anders throws a baseball straight up
from a height of 3 feet above the
ground. The initial velocity of the
baseball is 25 feet per second. What is
the height of the ball seconds after
it is thrown? Round your answer to the
nearest hundredth. (1 point) how many seconds

Answer 1

To find the height of the baseball at time \( t \) seconds after it is thrown, we can use the formula for the height of an object under the influence of gravity:

\[
h(t) = h_0 + v_0 t - \frac{1}{2} g t^2
\]

where:
- \( h(t) \) is the height at time \( t \),
- \( h_0 \) is the initial height (3 feet in this case),
- \( v_0 \) is the initial velocity (25 feet per second),
- \( g \) is the acceleration due to gravity (approximately \( 32 \) feet per second squared, directed downwards),
- \( t \) is the time in seconds.

Substituting the values into the formula:

\[
h(t) = 3 + 25t - \frac{1}{2} \cdot 32 t^2
\]

This simplifies to:

\[
h(t) = 3 + 25t - 16t^2
\]

So the formula for the height of the baseball at time \( t \) is:

\[
h(t) = -16t^2 + 25t + 3
\]

If you need the height at a specific time in seconds, please provide that time, and I can calculate it for you!