To determine the time it takes for the rocket to reach an altitude of 20,000 meters, we can use the equation representing the motion of the rocket under constant acceleration. The given equation is:
[tex]\[
\left(\frac{1}{2}\right) \times 400 \times t^2 = 20,000
\][/tex]
Let's solve this step-by-step:
1. First, simplify the equation:
[tex]\[
200 t^2 = 20,000
\][/tex]
2. Next, solve for [tex]\( t^2 \)[/tex] by dividing both sides of the equation by 200:
[tex]\[
t^2 = \frac{20,000}{200}
\][/tex]
3. Calculate the value of the right-hand side:
[tex]\[
t^2 = 100
\][/tex]
4. Finally, solve for [tex]\( t \)[/tex] by taking the square root of both sides:
[tex]\[
t = \sqrt{100}
\][/tex]
5. Simplify the square root:
[tex]\[
t = 10
\][/tex]
Therefore, the time it takes for the rocket to reach an altitude of 20,000 meters is 10 seconds.
The correct answer is:
B. 10 seconds
