Question

A rocket launched vertically from the ground with an initial veocity of 56ft?sec (A) Write a quadratic function that shows the height, in feet, of the rocket t seconds after it was launched.

(B)Graph h(t) on the coordinate plane.
(C) Use your graph from Part 3(b) to determine the rocket’s maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air.
Answer:
PLZZZZZZZZ HELP!!!!!!!!!!ASAP

Answer 1

The wording of this problem is a bit misleading. I am assuming what is being asked is the trajectory of a projectile, not a rocket. A rocket has an engine and continues being propelled. It is not possible to give a function describing its trajectory without knowing what the configuration is.

(A) As a projectile, it will have height changing according to the kinematic equation:

`h(t) = -(1)/(2)gt^2+v_0t=-4.9t^2+17.1t`

with g the gravitational acceleration and v0 the initial velocity (which needs to be transformed from 56ft/s to 17.7m/s. I am leaving out units in the final quadratic.

(B) Plot is attached

(C) Max height is roughly 15m. It took about 1.75s to reach that max height, which is half of the overall time in the air: 3.5s. These are all numbers estimated from the graph (visually). They can be calculated precisely from the quadratic in (A).