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1) What is the escape velocity (in m/s) for an object orbitingthe Earth at a hei

ID: 1675640 • Letter: 1

Question

1) What is the escape velocity (in m/s) for an object orbitingthe Earth at a height above the ground of 6.9E6 m? 2) A pitcher throws a 0.145-kg baseball to a batter at 36 m/s.The batter hits the ball straight back at the pitcher at 49 m/s.The amount of time that the bat and ball are in contact is 9.0E-3s. What is the force (in N, assumed to be constant) between theball and bat? 1) What is the escape velocity (in m/s) for an object orbitingthe Earth at a height above the ground of 6.9E6 m? 2) A pitcher throws a 0.145-kg baseball to a batter at 36 m/s.The batter hits the ball straight back at the pitcher at 49 m/s.The amount of time that the bat and ball are in contact is 9.0E-3s. What is the force (in N, assumed to be constant) between theball and bat?

Explanation / Answer

     (a)           Height abovethe ground, h = 6.9 x 106 m                                                 = 6900 km           Radius ofthe earth, R = 6400 km           Accelerationdue to gravity at the given height,                                                  g' = [ R / (R + h) ] 2 * g                                                      = [ 6400 / 13300 ]2 * 9.8                                                      = 2.27m/s2                                   Escapevelocity, Ve = ( 2 g' r )                                      = [ 2 g' ( R + h ) ]                                      = [ 2 * 2.27 * 13300 x 103 ]                                      = 7769.3 m/s                                      = 7.8 km/s      (b)           Mass of theball, m = 0.145 kg           Initialvelocity, Vi = - 36 m/s           Finalvelocity, Vf = 49 m/s           Time ofcontact, t = 9 x 10-3 s          Vi and Vf carry opposite signs because theyare in opposite directions           Force, F = ma    = m [ ( Vf - Vi ) / t]                      = ( 0.145 * 85 ) / ( 9 X 10-3 )                      = 1369.4 N