Question

A small rocket is fired from a launchpad 15 m above the ground with an initial velocity left angle 400,450,600 right angle ​m/s. A crosswind blowing to the north produces an acceleration of the rocket of 3 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.
a. Find the velocity and position vectors for t greater than or equal to 0.
b. Make a sketch of the trajectory.
c. Determine the time of flight and range of the object.
d. Determine the maximum height of the object.

Answer 1

Answer:

a)

v=<400, 450+3t, 600-9.81t> m/s

r=<400t, 450t+3$t^{2}$/2, 15+600t-9.81$t^{2}$/2> m/s

b) attach file

c) t=122.324s

d) z=18369.9854 m

Step-by-step explanation:

a)

The equation for velocity of each component is v=$v_{0}$+at, in this case the x-axis component has acceleration 0$\frac{m}{s^{2} }$, the y-axis component has acceleration 3$\frac{m}{s^{2} }$ and the z-axis component has -g$\frac{m}{s^{2} }$, where g=9.81$\frac{m}{s^{2} }$.

The equation for position of each component is  x=$x_{0}$+$v_{0}$t+a$t^{2}$/2,

with <$x_{0}$, $y_{0}$,$z_{0}$>=<0,0,15>.

c) This time is t when z=0, with positive sign.

d)Solving the equation $V_f^{2}$=$V_o^2$ + 2*a*(z-$z_{0}$) for z, with $V_f$=0.