The velocity, V feet per second, of a model rocket t seconds after launch is given by V = -32t...

Understanding the Question

We need to find the velocity of the rocket at t = 2 seconds.

Given the velocity formula: \(\mathrm{V = -32t + C}\)

• V is velocity in feet per second
• t is time in seconds after launch
• C is a positive constant

To find the velocity at t = 2, we’ll substitute into the formula:
\(\mathrm{V = -32(2) + C = -64 + C}\)

Since C is unknown, we need its exact value to answer the question.

Key insight: We must determine C to find the velocity at t = 2.

Analyzing Statement 1

Statement 1: "The rocket reaches its maximum height and begins descending 1.5 seconds after it was launched."

When any object reaches its maximum height, its velocity equals zero—it momentarily stops before falling back down.

At t = 1.5 seconds:

• \(\mathrm{V = 0}\) (at maximum height)

Substituting into \(\mathrm{V = -32t + C}\):

• \(\mathrm{0 = -32(1.5) + C}\)
• \(\mathrm{0 = -48 + C}\)
• \(\mathrm{C = 48}\)

Now we can find the velocity at t = 2:

• \(\mathrm{V = -32(2) + 48}\)
• \(\mathrm{V = -64 + 48}\)
• \(\mathrm{V = -16}\) feet per second

The negative velocity indicates the rocket is descending.

[STOP - Statement 1 is Sufficient!]

Since Statement 1 allows us to find \(\mathrm{C = 48}\), we can determine the exact velocity at t = 2.

This eliminates choices B, C, and E.

Analyzing Statement 2

Important: We now analyze Statement 2 independently, forgetting everything from Statement 1.

Statement 2: "The rocket’s initial velocity was 48 feet per second."

Initial velocity refers to the velocity at launch (t = 0).

At t = 0:

• \(\mathrm{V = 48}\) feet per second

Substituting into \(\mathrm{V = -32t + C}\):

• \(\mathrm{48 = -32(0) + C}\)
• \(\mathrm{48 = 0 + C}\)
• \(\mathrm{C = 48}\)

With \(\mathrm{C = 48}\), the velocity at t = 2:

• \(\mathrm{V = -32(2) + 48}\)
• \(\mathrm{V = -64 + 48}\)
• \(\mathrm{V = -16}\) feet per second

[STOP - Statement 2 is Sufficient!]

Statement 2 also allows us to find \(\mathrm{C = 48}\) and determine the exact velocity at t = 2.

This eliminates choice A.

The Answer: D

Each statement independently provides a different way to find \(\mathrm{C = 48}\):

• Statement 1: Uses the physics principle that velocity = 0 at maximum height
• Statement 2: Directly provides the initial condition

Once we know \(\mathrm{C = 48}\), we can calculate that the velocity at t = 2 is exactly -16 feet per second.

Answer Choice D: Each statement alone is sufficient.