Question 9

Explanation

Collision Condition

A collision between the rocket and the aircraft carrier occurs when both are at the same position at the same time. Therefore, we must equate the rocket's position function with the aircraft carrier's position function.

Determining the Collision Time

We rearrange the quadratic equation into standard form to solve for $t$.

Next, we factorize this quadratic equation. We need to find two numbers that multiply to $-4000$ and add up to $60$. These numbers are $100$ and $-40$.

From this factorization, we obtain two possible values for $t$:

Since time ($t$) cannot be negative, the valid value is $40$ seconds. Thus, the collision occurs exactly at $40$ seconds.