An object is kicked from a platform. The equation h = -4.9t^2 + 7t + 9 represents this situation, where...

1. INFER the mathematical meaning of the question

• The question asks for "the height from which the object was kicked"
• This means we need the initial height - the height at the very beginning
• In time-dependent equations, the initial condition occurs when \(\mathrm{t = 0}\)

2. SIMPLIFY by substituting \(\mathrm{t = 0}\)

• Given equation: \(\mathrm{h = -4.9t^2 + 7t + 9}\)
• Substitute \(\mathrm{t = 0}\):

\(\mathrm{h = -4.9(0)^2 + 7(0) + 9}\)

\(\mathrm{h = 0 + 0 + 9}\)

\(\mathrm{h = 9}\)

Answer: D. 9

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't connect "height from which object was kicked" with \(\mathrm{t = 0}\)

Many students see the equation \(\mathrm{h = -4.9t^2 + 7t + 9}\) and think one of the coefficients must represent the initial height. They might focus on the coefficient 7 (thinking it's related to initial velocity) or even 4.9 (thinking it's somehow the height), rather than recognizing that they need to evaluate the entire function at \(\mathrm{t = 0}\).

This may lead them to select Choice C (7) or Choice B (4.9)

Second Most Common Error:

Missing conceptual knowledge: Not understanding what \(\mathrm{t = 0}\) represents in context

Some students might understand they need an initial value but aren't clear on what \(\mathrm{t = 0}\) means in a real-world context. They might randomly guess or get confused about which variable represents what.

This leads to confusion and guessing among the answer choices.

The Bottom Line:

This problem tests whether students can translate between physical meaning ("initial height") and mathematical representation (\(\mathrm{t = 0}\) in a time-dependent function). The calculation itself is straightforward once this connection is made.