1) An anxious mouse is scurrying back and forth. Starting at a distance of 1 meter away from the cheese, he starts to move toward his tasty prize. When he gets to į meter away, he changes
direction and starts moving away from the cheese. After meter, he changes direction and
moves toward the cheese. After meter, he starts moving away again, and so on.
How far away from the cheese is the mouse when he begins to make his nth turn?

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?