To find the height of the rocket after 1.5 seconds, we need to substitute \( t = 1.5 \) into the function \( t(h) \) and solve for \( h \).
The function is given as: \[ t(h) = \pm\sqrt{h - 67}/-16 + 2 \]
First, rearranging this equation to solve for \( h \), we start with: \[ t(h) = \frac{\sqrt{h - 67}}{-16} + 2 \]
To find \( h \) when \( t = 1.5 \), we set: \[ 1.5 = \frac{\sqrt{h - 67}}{-16} + 2 \]
Now, isolating the square root term: \[ 1.5 - 2 = \frac{\sqrt{h - 67}}{-16} \] \[ -0.5 = \frac{\sqrt{h - 67}}{-16} \]
Multiplying both sides by \(-16\): \[ 8 = \sqrt{h - 67} \]
Now squaring both sides: \[ 64 = h - 67 \]
Adding 67 to both sides: \[ h = 64 + 67 = 131 \]
Thus, the height of the rocket after 1.5 seconds is \( h = 131 \) feet.
Since this value isn't among the answer options provided (39 feet, 63 feet, 75 feet, 129 feet), let's reevaluate the initial expression to ensure no errors occurred or clarify information provided.
From the calculations, if \( t \approx 1.5 \), the model provided may have constraints or may not fit realistic boundaries, but using the equation given led us to a height of 131 feet.
If the options must be considered and they were valid, please confirm the function's accuracy or applicable details; otherwise, an interpretation error might have been present originally.