A rocket is launched from rest at an angle of 700 with respect to the ground. Fo

Question

A rocket is launched from rest at an angle of 700 with respect to the ground. For the first 2 minutes the boosters fire and cause the rocket to accelerate at 5.25 m/s this is the actual acceleration of the space shuttle after launch). Then the boosters cut off and the rocket comes back down to earth. (Assume that the rocket has all its engines turned off all the way back down and miraculously lands perfectly instead of crashing) Draw a diagram showing the motion over the entire flight of the rocket. Label known and unknown variables at important points in the motion (use logic to determine what these points are!). What is the rocket's velocity vector when the boosters turn off? Give your answer with i and j notation What is the height of the rocket when the boosters turn off? From the time the rocket is launched, how long will it take for the rocket to get back to earth? What is the speed of the rocket when it lands?

Explanation / Answer

Final vertical velocity = (5.25 * sin70 * 120)

                                  = 592 m/s

Final horizontal velocity = (5.25 * cos70 * 120)

                                  = 215.47 m/s

Thus, final velocity = (215.47 i + 592 j) m/s

height of rocket = (592)2/(2 * 5.25 * sin70)

                           = 35519.62 m

time taken = sqrt(2 * 35519.62/5.25 * sin70) + sqrt(2 * 35519.62/9.8)

                    = 205 s

speed of rocket =    (215.47 i + 857.2 j) m/s

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