A ball of mass m is thrown upwards with a velocity v. If air exerts an average resisting force R, the velocity with which the ball returns to the thrower is ?
answer is v(mg - R/ mg + R)^1/2please explain how !!

Question

A ball of mass m is thrown upwards with a velocity v If air exerts
an average resisting force R, the velocity with which the ball
returns to the thrower is ?
answer is v(mg - R/ mg + R)1/2 please explain how !!

Vaibhav T. · Accepted Answer

Dear Student,

Lets divide the journey of ball in two parts, upward and downward :For upward journey :From work-energy theorem,work done, W=∆KE-Fh-mgh=-12mv2Fh+mgh=12mv2  
 1For downward journey :Since F is a resistance force, so it will change its direction
W=12mv12-Fh+mgh=12mv12  
 2Divide 1 and 2, we getFh+mghmgh-Fh=12mv212mv12v12=v2mg-Fmg+Fv1=vmg-Fmg+F

A ball of mass m is thrown upwards with a velocity v. If air exerts an average resisting force R, the velocity with which the ball returns to the thrower is ? answer is v(mg - R/ mg + R)1/2 please explain how !!

A ball of mass m is thrown upwards with a velocity v. If air exerts an average resisting force R, the velocity with which the ball returns to the thrower is ?
answer is v(mg - R/ mg + R)^1/2please explain how !!