Question

A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius R_E gives the radial distance (from the Earth's center) the projectile reaches if a) its initial speed is 0.365 of the escape speed from Earth and b) its initial kinetic energy is 0.365 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?

Answer 1

(a) escape speed from earth's surface Ve=2g R vel of projectile = 0.365 J2gR ovi ewing conservation of energy - GM + mv² - C More a ale) = - + CAMP - (0.3653 (298) + GR Rth his = 0.866 ) Ithe-1.15 h = 0.15 h = 0,158, & KE required to escape = 1 mV e 2 = mg R KE of object = 0.365 mg R using conseunt of energy - CMM + 0.365 mg R= - GMm. -gR+ 0.3659R -GR Rrith/R) 0.635 CithlR) 0.635 = - ithir Th=0.578 (c) mechanical E = KE A Pt Scanned with CamScanner - GMm & mar