To find the height at which the toy rocket was launched, we need to evaluate the height function at the moment of launch. The rocket was launched at time \( t = 0 \). The height function is given as:
[tex]\[ h(t) = -16 t^2 + 200 t + 50 \][/tex]
We substitute \( t = 0 \) into the height function:
[tex]\[ h(0) = -16(0)^2 + 200(0) + 50 \][/tex]
Since \( 0^2 = 0 \) and \( 200 \times 0 = 0 \), the expression simplifies to:
[tex]\[ h(0) = 50 \][/tex]
Therefore, the height at which the rocket was launched is:
[tex]\[ 50 \, \text{ft} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{50 \, \text{ft}} \][/tex]
