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.

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

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

with <[tex]x_{0}[/tex], [tex]y_{0}[/tex],[tex]z_{0}[/tex]>=<0,0,15>.

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

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