Answered

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A toy rocket is launched straight up from the top of a building. The function that models the height as a function of time is [tex]h(t) = -16t^2 + 200t + 50[/tex]. At what height was the rocket launched?

A. 16 ft
B. 50 ft
C. 25 ft
D. 200 ft

Sagot :

GinnyAnswer
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]
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