(*100 POINTS*) BE FAIR PLSIn order to host track and field competitions, a 400-meter track needs to be created. A typical Olympic track looks like the one on the picture.

a) Show that the runner who runs in the inside lane runs 400 meters.
b) All other runners in a 400 meters race start a little further ahead since their lane is a little longer. If the radius of lane 2 (the one beside the inside lane) is 37.92 meters, find how much of a stagger (head start) the lane 2 runner should be given. Round your answer to the nearest hundredth.

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?