A toy rocket is launched from a platform 1.4 meters above the ground in such a way this it’s height , h (in meters) after t seconds is given by the equation h=-4.9t^2+9.1t + 1.4. How long will it take for the rocket to hit the ground?

1 answer

To find out when the rocket will hit the ground, we need to determine the time at which the height, h, is equal to 0.

The equation given is h = -4.9t^2 + 9.1t + 1.4.

Setting h to 0, the equation becomes 0 = -4.9t^2 + 9.1t + 1.4.

To solve this equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac))/(2a)

In this equation, a = -4.9, b = 9.1, and c = 1.4.

Substituting these values into the quadratic formula:

t = (-(9.1) ± √((9.1)^2 - 4(-4.9)(1.4))) / (2(-4.9))

Simplifying this equation:

t = (-9.1 ± √(83.41 + 27.44)) / (-9.8)

t = (-9.1 ± √110.85) / (-9.8)

Now we have two possible solutions:

t ≈ (-9.1 + √110.85) / (-9.8)
t ≈ (-9.1 - √110.85) / (-9.8)

Calculating these two solutions:

t ≈ (-9.1 + 10.53) / (-9.8)
t ≈ 1.43 / (-9.8)
t ≈ -0.146

t ≈ (-9.1 - 10.53) / (-9.8)
t ≈ -19.63 / (-9.8)
t ≈ 2

Since time cannot be negative in this context, the rocket will hit the ground after approximately 2 seconds.