To find the height of the rock at 1 second after it leaves her hand, Samantha would need to use the height equation for projectile motion. A typical height equation can be modeled as:
\[ h(t) = -16t^2 + vt + h_0 \]
where \( h(t) \) is the height at time \( t \), \( v \) is the initial velocity, and \( h_0 \) is the initial height.
In this case, from the given response context, it looks like we are using:
- Initial height \( h_0 = 6 \) feet
- Initial velocity \( v = 32 \) feet per second (which could be inferred if we assume standard projectile motion equations).
Now, we want to find the height of the rock at \( t = 1 \) second:
\[ h(1) = -16(1)^2 + 32(1) + 6 \]
Calculating the expression:
- Calculate \( -16(1)^2 = -16 \)
- Calculate \( 32(1) = 32 \)
- Add the initial height: \( -16 + 32 + 6 \)
Combine those:
\[ -16 + 32 = 16 \] \[ 16 + 6 = 22 \]
So, Samantha correctly found that the height of the rock at 1 second after it leaves her hand is 22 feet.
Thus, the correct response is:
Samantha substituted \( t = 1 \) into the expression to get \( h(1) = -16(1)^2 + 32(1) + 6 = 22 \).