Answer the following

es Thinking Total /10 /10 /20 Question 1: A rubber ball bounces to 2/3 of its height when dropped on a hard surface. (a) Determine a recursive formula for the sequence of successive heights. 12 (b) Determine an explicit formula for the sequence of successive heights. 12 (c) Suppose the ball is dropped from 27m, what is the total distance travelled by the ball after 11 bounces? /2T Question 2: A spacecraft leaves an orbiting space station to descend to the planet below. The spacecraft descends 64km during the first second and then engages its reverse thrusters to slow down its descent. It travels 7 fewer kilometers during each second afterward (a) If the spacecraft stops after 8s, how far did it descend? 12T (b) If the space station is at a height of 300km, how long will it take for the spacecraft to reach the surface of the planet? /2T