Conservation of Momentum Problem?

[r_swayze]

A cat stands on a skateboard that moves without friction along a level road at a constant velocity of 2.00 m/s. She is carrying a number of books. She wishes to stop, and does so by hurling a 1.20 kg book horizontally forward at a speed of 15.0 m/s with respect to the ground. (a) What is the total mass of the cat, the skateboard, and any remaining books? (b) What mass book must she now throw at 15.0 m/s with respect to the ground to move at −2.00 m/s?

I got the answer to part A, here is my work for part A:

m₁v_i1 + m₂v_i2 = m₁v_f1 + m₂v_f2

m₁ = total mass of the cat, the skateboard, and any remaining books
v_i1 = 2.0 m/s
v_f1 = 0 m/s
m₂ = 1.2 kg book
v_i2 = 2.0 m/s
v_f2 = 15.0 m/s

m₁v_i1 = -m₂v_i2 + m₁v_f1 + m₂v_f2

m₁ = (-m₂v_i2 + m₁v_f1 + m₂v_f2) / v_i1

m₁ = (-1.2*2.0 + m₁*0 + 1.2*15.0) / 2.0
m₁ = 7.8 kg

Now for part B, I thought I had the correct answer but apparently it is wrong. Here is my work:

From part a
m₁ + m₂ = total mass of of the cat, the skateboard, and any remaining books
m₁ + m₂ = 7.8 kg + 1.2 kg
m₁ + m₂ = 9 kg = m_t

m_tv_i = m₁v_f1 + m₂v_f2

9*2 = m₁*-2.0 + m₂*15.0
18 = -2m₁ + 15m₂

So m₁ + m₂ should equal to total mass = 9 kg

m₁ + m₂ = 9
m₁ = 9 - m₂

Plug into equation

18 = -2(9 - m₂) + 15m₂
18 = -18 + 2m₂ + 15m₂
36 = 17m₂
m₂ = 2.11 kg

Have I erred somewhere? If you plug in 2.11 kg and 6.88 kg, it comes out roughly correct. Should I be using 9 kg in part B?

Any help is much appreciated

 

[ehild]

Your solution must be correct but a rounding error. m₂=2.1176 kg, should be rounded to 2.12 kg.

ehild

 

[r_swayze]

Your solution must be correct but a rounding error. m₂=2.1176 kg, should be rounded to 2.12 kg.

ehild

I tried 2.12 as well, it was still incorrect. Is my method correct?

 

[ehild]

I think, your solution is correct, but we may misunderstand the text. Maybe it asks the mass of book that the cat has to throw after it has stopped, to gain -2 m/s velocity. Try it...

But also the official solution can be wrong.

ehild