Asmall rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 right angle m/s. a cross wind blowing to the north produces an acceleration of the rocket of 2.5 m divided by s squared. assume the x-axis points east, the y-axis points north, the positive z-axis is vertical (opposite g), and the ground is horizontal. answer parts a through d.
find:
a/ velocity and position vectors. b/ determine the time of the flight and range of the rocketc/ determine the maximum hight of the rocket.

Let denote the rocket's position, velocity, and acceleration vectors at time .

We're given its initial position

and velocity

Immediately after launch, the rocket is subject to gravity, so its acceleration is

where .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

and

b. The rocket stays in the air for as long as it takes until , where is the -component of the position vector.

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

c. The rocket reaches its maximum height when its vertical velocity (the -component) is 0, at which point we have

answer: apothems is your answer

step-by-step explanation: hope u get it right