Question 1) A 2.5 kg ball and a 5.0 kg ball have an elastic collision. The 2.5kg

Question

Question 1)

A 2.5 kg ball and a 5.0 kg ball have an elastic collision. The 2.5kg ball was at rest and the other ball had a speed of 3.5 m/s. Whatis the kinetic energy of the 2.5 kg ball after thecollision?

I used the conservation of momentum

5 x 3.5 = 17.5

so 2.5(v) = 17.5

v = 7 m/s

kinetic energy which is 1/2 m v^2

.5 x 2.5 x 7^2

= 61.25 J

I got 61.25 J, however the answers have to be..

a) 1.7 J b) 8.1 J c)3.4 J d) 14 J e)27 J

What is the answer? and how do you come to it?

2nd Question

A 5.0 kg boy runs at a speed of 10.0m/s and jumps onto a cart. Thecart is initially at rest. If the speed, with the boy on the cart,is 2.50 m/s, what is the mass of the cart?

mv + m2v2 = m'v'

(5)(10) + m2(0) = (M2 + 5) (2.5)

50 = 2.5M + 12.5

M = 15 kg

is what I did, but the answers have to be either....

a) 150 J b) 210 J c) 175J d) 260 J e) 300 J

what is the answer and what am I doing wrong? can someonehelp??

thanks

Explanation / Answer

A 2.5 kg ball and a 5.0 kg ball have anelastic collision. The 2.5 kg ball was at rest and the other ballhad a speed of 3.5 m/s. What is the kinetic energy of the 2.5 kg ball after thecollision? I used the conservation of momentum (good!) m1u1= m1V1 +m2V2 We have 2 unknownsV1and V2 and onlyone equation V1 = (m1u1-m2V2 )/m1 . kinetic energy which is 1/2 m v^2(Yes) Now we use law of conservation of energy since it was anelastic collision 0.5m1u12=0.5 m1V12 +0.5m2V22 m1u12=m1V12+ m2V22 Substitute V1 = (m1u1-m2V2 )/m1intom1u12=m1V12 +m2V22 we have m1u12= m1[(m1u1- m2V2)/m1]2 + m2V22______________- m1u12=m1 [(m1u1-m2V2 )/m1]2 +m2V22m12u12= [(m1u1-m2V2 )]2 + m2m1V22m12u12=(m1u1)2 -2(m1u1 m2V2) + (m2V2 ) 2 + m2m1V22 Now do algebra and solve for V2 and use that in Ke2=m2V22 a) 1.7 J b)8.1 J c) 3.4 J d)14 J e) 27J What is the answer? and howdo you come to it? 2ndQuestion A 5.0 kg boy runs at a speed of 10.0m/s and jumps onto a cart. Thecart is initially at rest. If the speed, with the boy on the cart,is 2.50 m/s, what is the mass of the cart? Nowm1u1=(m1 + m2)V m2= (m1u1 -m1 V)/Vm2= (5x 10 - 5x2.5)/2.5= 15kg        Than should do it. Please let me know if you have any questions a) 150J b) 210 J c) 175 J d)260 J e) 300 J what is the answer and what am I doing wrong? can someonehelp??

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