The function \( h(t) = -16t^2 + 75t \) gives the height of a ball thrown into the air at time \( t \) seconds.
To determine what \( h(5) \) represents, we need to substitute \( t = 5 \) into the function.
Calculating \( h(5) \):
\[ h(5) = -16(5^2) + 75(5) \] \[ = -16(25) + 375 \] \[ = -400 + 375 \] \[ = -25 \]
The value \( h(5) = -25 \) means that at 5 seconds after the ball is thrown, the height of the ball is -25 feet. This indicates that the ball has fallen below the starting point (assuming the starting point is at ground level, which is typically the case in such problems).
So, \( h(5) \) represents the height of the ball relative to the ground at 5 seconds, and in this case, it indicates that the ball is 25 feet below the ground level.