Question

2. A rocket of mass m is fired vertically from the Earth, with an initial speed U. It rises to a height R/2 before falling back to Earth, where R is the radius of the Earth. Calculate U in terms of G, M (the Earth's mass) and R. The rocket is fired with the same initial speed, but this time at an angle 45° to the horizontal. Calculate its angular momentum J and total energy E, and use these to calculate a and e for the orbit. Find the polar coordinates of A and B, the points where the orbit intersects with the Earth's surface. Earth apogee h=0.45 R AB 0.49 R What is the maximum height h that this rocket reaches, and how far does it travel, i.e. what is the length of the arc AB? Give your answers in terms of R. (The launch angle in the sketch is not 45°.) What is the maximum range AB for a rocket launched with speed U? What is the launch angle for maximum range, and what will the greatest height be?

Answer 1

82 3 3 R B R 3 R 3 2a

2. Ra 3 R.

h= 0.31R