Question

an object is thrown from a roof 200 feet above the ground, the height of the object in feet t seconds after being thrown is given by the function h(t) = 16 t^2 + 8t + 200
What is the height of the object 2 seconds after being thrown
A 120 feet
B 152 feet
C 184 feet
D 192 feet

Answer 1

To find the height of the object 2 seconds after being thrown, we need to evaluate the function \( h(t) \) at \( t = 2 \).

Given the function:
\[
h(t) = -16t^2 + 8t + 200
\]

we substitute \( t = 2 \):
\[
h(2) = -16(2)^2 + 8(2) + 200
\]

Calculating step-by-step:

1. Calculate \( (2)^2 \):
\[
(2)^2 = 4
\]

2. Multiply by -16:
\[
-16 \times 4 = -64
\]

3. Calculate \( 8(2) \):
\[
8 \times 2 = 16
\]

4. Now substitute back into the equation:
\[
h(2) = -64 + 16 + 200
\]

5. Simplify:
\[
-64 + 16 = -48
\]
\[
-48 + 200 = 152
\]

Therefore, the height of the object 2 seconds after being thrown is **152 feet**, which corresponds to option **B**.