- 6 An Alien Spacecraft Wishes To Visit Earth But In Order To Do So It Must First Escape Its Home Planet D Qar D Qar Ha 1 (100.77 KiB) Viewed 38 times
6. An alien spacecraft wishes to visit Earth, but in order to do so it must first escape its home planet D'Qar. D'Qar has a mass 3 x 1024 kg and radius 7 x 106 m. (a) Write down an equation for total mechanical energy E of an object in a circular orbit around a planetary body, and use it to derive an equation for the escape velocity of the alien spacecraft. (b) Calculate the velocity the alien spacecraft needs to obtain to leave its home world. (c) Briefly explain what will happen if the alien spacecraft is launched with a velocity greater than the escape velocity. What type of orbit will the spacecraft follow? [2] [4] 7. A plank is 10 m long and has a mass of 20 kg. It is placed on horizontal ground at the edge of a vertical river bank, so that 2 m of the plank is projecting over the edge, as shown in Figure 1. 10 m 2 m Figure 1: A plank balanced over a stream. [2] [2] (a) A child of mass 10 kg stands at the left edge of the plank. Calculate the centre of mass of the child-plank system. (b) What assumptions you have made in calculating the centre of mass? (c) The child urges his father of mass 70 kg to stand at the right end of the plank, stating that that the plank won't tip up. Show that the child is correct. If the plank moved so that 3 m is projecting over the edge, whilst the child and his father remain at both ends, determine what will happen. [3] [3]