Question

Jaha has designed a rocket. She determines the initial velocity of her rocket is 36 meters per second. She uses the function h(t) = - 9.8t ^ 2 + 36t to find the height, h(t) based on time, t, in seconds. Jana wants to know approximately when her rocket will be at the following heights:

24 Meters
36 Meters

Answer 1

To find when the rocket will be at a certain height, we can set the equation for height, h(t), equal to the given height and solve for t.

For 24 meters:

-9.8t^2 + 36t = 24

-9.8t^2 + 36t - 24 = 0

We can solve for t using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -9.8, b = 36, and c = -24. Plugging in these values, we get:

t = (-36 ± sqrt(36^2 - 4(-9.8)(-24))) / 2(-9.8)

t ≈ 1.87 seconds or t ≈ 3.14 seconds

So the rocket will be at a height of 24 meters approximately 1.87 seconds after launch and again approximately 3.14 seconds after launch.

For 36 meters:

-9.8t^2 + 36t = 36

-9.8t^2 + 36t - 36 = 0

Using the quadratic formula again, we get:

t = (-36 ± sqrt(36^2 - 4(-9.8)(-36))) / 2(-9.8)

t ≈ 1.16 seconds or t ≈ 3.66 seconds

So the rocket will be at a height of 36 meters approximately 1.16 seconds after launch and again approximately 3.66 seconds after launch.