Question 12

Explanation

Determining the Time of Impact

The impact occurs when both objects are at the same position. Therefore, we need to equate the position equations of the rocket and the aircraft carrier to find the time of the event.

Next, we factor the quadratic equation to find the value of $t$.

From the factorization above, we obtain two solutions: $t = -100$ or $t = 40$. Since time cannot be negative, we take the positive value.

Calculating the Position of Impact

After finding the time of impact, we can calculate the position by substituting $t = 40$ into either position equation. We use the aircraft carrier's equation as it is simpler.

Finally, we convert the unit from meters to kilometers.

Thus, the position when the rocket exactly hits the aircraft carrier is $2.4$ km.