The height of the rocket can be represented by the equation:
y = -3x^2 + 20x + 7
To find the time at which the rocket will land on the ground, we need to find the value of x when the height, y, equals zero. This is because the rocket will be on the ground when its height is zero.
So, we can write:
0 = -3x^2 + 20x + 7
To solve for x, we can use the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
In this case, a = -3, b = 20, and c = 7. Substituting these values into the quadratic formula, we get:
x = [-20 ± sqrt(20^2 - 4(-3)(7))] / 2(-3)
Simplifying this expression, we get:
x = [-20 ± sqrt(400 + 84)] / (-6)
x = [-20 ± sqrt(484)] / (-6)
x = [-20 ± 22] / (-6)
Therefore, the possible values of x are:
x = (-20 + 22) / (-6) = -1/3 or x = (-20 - 22) / (-6) = 7
The value of x = -1/3 is not a valid answer because time cannot be negative. Therefore, the rocketwill land on the ground after 7 seconds.
Thus, the time at which the rocket will land on the ground is:
7 seconds.