explain how to find the time it takes for a rocket following the path of the parametric equations, x = 3t 2 and y = -9t + 18, to hit the ground
if y is the height, then all you need is
y=0
-9t+18 = 0
t = 2
so, it takes 2 seconds to hit the ground.
To find the time it takes for a rocket following the path of the parametric equations x = 3t^2 and y = -9t + 18 to hit the ground, we need to determine when the y-coordinate becomes zero.
Step 1: Set the y-coordinate equation equal to zero and solve for t.
-9t + 18 = 0
Step 2: Solve the equation for t.
Subtracting 18 from both sides, we get:
-9t = -18
Dividing both sides by -9, we get:
t = 2
Therefore, the rocket will hit the ground at t = 2.
To find the time it takes, we substitute the value of t back into either the x-coordinate or y-coordinate equation. Let's use the x-coordinate equation:
Step 3: Substitute t = 2 into x = 3t^2.
x = 3(2^2)
x = 3(4)
x = 12
Therefore, the rocket will hit the ground at x = 12. Hence, it will take 2 units of time for the rocket to hit the ground following the given parametric equations.