An asteroid of massm = 7.5 x 1012 kg has two rocket thrusters attached to it. One thruster supplies a force with 3: and y- components F1 = (8.0 X 107, 7.0 X 107) N while the other supplies a force with :13- and ycomponents F2 = (4.0 x 107, 2.0 x 107) N. (You may ignore the mass of the rocket thrusters and their fuel.) Give all your answers in scientic notation to an appropriate number of signicant gures. (8) (i) (ii) (iii) Preparation: Draw a sketch showing the two forces acting on the asteroid. Your sketch should be drawn (approximately) to scale. Use your sketch to estimate (without calculation) the resultant force on the asteroid. Include the resultant force on your sketch. Working: What is the magnitude of the resultant force and in which direction does it act? Checking: Compare your calculations from (a) (ii) with your sketch from (a)(i). Do your results agree? (b) At what distance from the Earth, in kilometres, would the force calculated in (a) have the same magnitude as that due to the gravitational attraction between the asteroid and the Earth? (C) (i) (ii) What is the magnitude of the acceleration of the asteroid produced by the thrusters and in which direction does it act? If the constant force calculated in (a) acts in the same direction as the asteroid's motion, calculate the time required to change the speed of the asteroid by 1 ms'1 and therefore show that this is about 16 hours