When a ball of mass m is dropped from rest from a height h , its speed just befo

Question

When a ball of mass m is dropped from rest from a heighth, its speed just before landing is v. Now,suppose a second ball of mass 4m is dropped from rest froma height h/4. (A) Just before ball 2 lands, is its speed4v,2v,v, v/2, or v/4? (b) Choose the bestexplanation from among the following: I. The factor of 4 cancel; therefore , the landing speed isthe samee II. The two balls land with the same kinetic energy;therefore, the ball mass 4m has the speed v/2. III. Reducing te height by a factor of 4 reduces the speed bya factor of 4 I'm thinking the higher the ball, the more the velocity remainconstant, but the energy is increased When a ball of mass m is dropped from rest from a heighth, its speed just before landing is v. Now,suppose a second ball of mass 4m is dropped from rest froma height h/4. (A) Just before ball 2 lands, is its speed4v,2v,v, v/2, or v/4? (b) Choose the bestexplanation from among the following: I. The factor of 4 cancel; therefore , the landing speed isthe samee II. The two balls land with the same kinetic energy;therefore, the ball mass 4m has the speed v/2. III. Reducing te height by a factor of 4 reduces the speed bya factor of 4 I'm thinking the higher the ball, the more the velocity remainconstant, but the energy is increased

Explanation / Answer

       Given that the initial heightof the body of mass m is h       Landing speed of the mass m is v        initial height of the body ofmass 4m is h/4 ----------------------------------------------------------------- If the body of mass m released from height h , thelanding speed is                  v = (2gh) Then speed of the body of mass 4 m is              V = [ 2g(h/4) ]                    = ( gh / 2)                       = v / 2

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