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arlik [135]
2 years ago
11

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.

Mathematics
1 answer:
vivado [14]2 years ago
3 0

Answer:

a)

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

r=<400t, 450t+3t^{2}/2, 15+600t-9.81t^{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+at^{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.

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