To find the height of the object 2.5 seconds after it was dropped using the equation \( h(t) = -9.8t^2 + 100 \), we substitute \( t = 2.5 \) into the equation.
\[ h(2.5) = -9.8(2.5)^2 + 100 \]
First, we calculate \( (2.5)^2 \): \[ (2.5)^2 = 6.25 \]
Now substitute this back into the equation: \[ h(2.5) = -9.8 \times 6.25 + 100 \] \[ h(2.5) = -61.25 + 100 \] \[ h(2.5) = 38.75 \]
Thus, the height of the object 2.5 seconds after it was dropped is 38.75 meters.