An Alaska rescue plane drops a package of supplies to a group of lost explorers. If the plane travels horizontally at 40 m / s, and at a height of 100 m on the floor. Where does the package fall relative to where it was released? How much How long does it take to reach the ground? How fast does it hit the ground?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .