Answer:
3.33 minutes
Explanation:
h = rt - 4.9t^2
In this case, the rocket is launched upward, so the initial velocity (r) is positive 1960 m/s. The rocket will fall to the ground when the height (h) becomes zero.
0 = 1960t - 4.9t^2
To solve this quadratic equation, we can set it equal to zero and use the quadratic formula:
4.9t^2 - 1960t = 0
Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 4.9, b = -1960, and c = 0. Plugging in these values:
t = (-(-1960) ± √((-1960)^2 - 4 * 4.9 * 0)) / (2 * 4.9)
Simplifying further:
t = (1960 ± √(3841600)) / 9.8
t = (1960 ± 1960) / 9.8
t = 1960 / 9.8 = 200
So, the rocket will fall to the ground after 200 seconds. To convert this to minutes, divide by 60:
200 seconds / 60 = 3.33 minutes (approximately)
Therefore, the rocket will fall to the ground after approximately 3.33 minutes.