A father racing his son has half the kinetic energy of the son, who has two-fifths the mass of the father. The father speeds up by 2.5 m/s and then has the same kinetic energy as the son.
(a) What is the original speed of the father?
(b) What is the original speed of the son?
I tried and tried and tried, but I am not getting the right answer. I am running out of submissions so I am getting desperate, please help! Will rate best.
(a) What is the original speed of the father?
(b) What is the original speed of the son?
I tried and tried and tried, but I am not getting the right answer. I am running out of submissions so I am getting desperate, please help! Will rate best.
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Let the dad's initial ke = 1/2 Mu^2 = 1/2 1/2 mU^2 = 1/2 KE, where KE = 1/2 mU^2 is the son's. m = 2/5 M. EQN 1
Then ke' = 1/2 M(u + 2.5)^2 = 1/2 mU^2 = 2/10 MU^2 = KE EQN2.
(a) So u^2 + 5u + 6.25 = 4/10 U^2 and U^2 = 2.5(u^2 + 5u + 6.25).
Then putting this into the first equation above, we have 1/2 Mu^2 = 1/4 (2/5)M2.5(u^2 + 5u + 6.25)
u^2 = 1/2 2/5 2.5 (u^2 + 5u + 6.25) = 1/2u^2 + 2.5u + 3.15, then forming the quadratic, we have
0 = 1/2 u^2 - 2.5u - 3.13; so that, using a quadratic calculator, we have u = 6.04 mps ANS.
(b) And from the first equation, we have U^2 = (5/2)4/2 u^2 = 5u^2 and U = sqrt(5)*6.04 = 13.5 mps. ANS.
Then ke' = 1/2 M(u + 2.5)^2 = 1/2 mU^2 = 2/10 MU^2 = KE EQN2.
(a) So u^2 + 5u + 6.25 = 4/10 U^2 and U^2 = 2.5(u^2 + 5u + 6.25).
Then putting this into the first equation above, we have 1/2 Mu^2 = 1/4 (2/5)M2.5(u^2 + 5u + 6.25)
u^2 = 1/2 2/5 2.5 (u^2 + 5u + 6.25) = 1/2u^2 + 2.5u + 3.15, then forming the quadratic, we have
0 = 1/2 u^2 - 2.5u - 3.13; so that, using a quadratic calculator, we have u = 6.04 mps ANS.
(b) And from the first equation, we have U^2 = (5/2)4/2 u^2 = 5u^2 and U = sqrt(5)*6.04 = 13.5 mps. ANS.
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