A hiker leaves the Visitor Center traveling East-by-North East. She hikes 13 miles before twisting her ankle and calling back to the Visitor Center. Rescue Ranger A recommends taking
the Northbound service road to rescue the hiker. Rescue Ranger B recommends taking the
Eastbound service road to rescue the hiker.
Which route is shortest? Support your answer.
What is the total distance traveled by the hiker on her walk and rescue?

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?