My Math Forum conservation of momentum

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 March 18th, 2017, 09:37 PM #1 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 conservation of momentum I've done 3 and 4 just want a clarification that its right Q3) Maxim, of mass 70kg, is running at 3.5ms-1 when he jumps on a skateboard, of mass 2.2kg, travelling at 0.8 ms-1 in the same direction. i. Calculate their new combined velocity. Q4) Maxim is on his skateboard again travelling at 6ms-1 in the opposite direction to which his hat is pointed. He then leaps off the skateboard. If the skateboard’s velocity after the leap was -0.5ms-1, find Maxim’s velocity post leap. (Mass of skateboard = 3kg, mass of Mr VT = 70kg). I need help with this question Q5) Maxim is on his skateboard again, travelling at 4ms-1 to the right. He then leaps off the skateboard. If the distance between Maxim and the skateboard was increasing at a rate of 4 metres per second, find Maxim’s velocity post leap. (Mass of skateboard = 3kg, mass of Mr vT = 70kg). (There are two solutions to this problem, explain what both mean in this situation).
 March 19th, 2017, 04:50 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416 Post your calculations for Q3 & Q4 if you want verification. Q5. $\vec{p_0}=\vec{p_f}$ $(M+m)v_0 = Mv_{1f}+mv_{2f}$ Case 1: $v_{2f}-v_{1f} = 4$ if the skateboard is ahead of Maxim post separation Case 2: $v_{1f}-v_{2f} = 4$ if Maxim is ahead of the skateboard post separation Solve the system of equations for each case Thanks from Posher Last edited by skeeter; March 19th, 2017 at 05:21 AM.
 March 19th, 2017, 12:35 PM #3 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 I get most of it by could you go into a bit more detail into how you got the first equation like how did u derive v0 Also for question 3 I got 3.2ms^-1 and for question 4 I got 6.29ms^-1 Last edited by Posher; March 19th, 2017 at 12:52 PM.
March 19th, 2017, 01:58 PM   #4
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Quote:
 Q3) Maxim, of mass 70kg, is running at 3.5ms-1 when he jumps on a skateboard, of mass 2.2kg, travelling at 0.8 ms-1 in the same direction. i. Calculate their new combined velocity. ... for question 3 I got 3.2ms^-1
Q3. I get 3.4 m/s

Quote:
 Q4) Maxim is on his skateboard again travelling at 6ms-1 in the opposite direction to which his hat is pointed. He then leaps off the skateboard. If the skateboard’s velocity after the leap was -0.5ms-1, find Maxim’s velocity post leap. (Mass of skateboard = 3kg, mass of Mr VT = 70kg). ... for question 4 I got 6.29ms^-1
if the hat is pointed in the negative direction (Maxim moving in the positive direction), then Maxim's $v_f = 6.3 \, m/s$

Q5.

Quote:
 Maxim is on his skateboard again, travelling at 4ms-1 to the right.
$\vec{p_0} = (M+m)v_0$

$M = 70 \, kg$, $m = 3 \, kg$, $v_0 = 4 \, m/s$

Quote:
 He then leaps off the skateboard.
$\vec{p_f} = Mv_{1f} + mv_{2f}$

Quote:
 the distance between Maxim and the skateboard was increasing at a rate of 4 metres per second
either $v_{2f} - v_{1f} = 4$ if the skateboard is farther right after they separate, or $v_{1f} - v_{2f} = 4$ if Maxim is farther right after separation.

case 1 ... $v_{2f} - v_{1f} = 4 \implies v_{2f} = v_{1f}+4$

substitute for $v_{2f}$ in the total momentum conservation equation given inthe previous post ...

$(M+m)v_0 = Mv_{1f} + m(v_{1f}+4)$

$(M+m)v_0 = Mv_{1f} + mv_{1f}+ 4m$

$(M+m)v_0 - 4m = v_{1f}(M+m)$

$\dfrac{(M+m)v_0 - 4m}{M+m} = v_{1f}$

sub in your given values to calculate $v_{1f}$, then add 4 to get $v_{2f}$

... same idea for case 2.

 March 19th, 2017, 09:07 PM #5 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 skeeter I'm pretty sure even though you got slightly different answers to me in q3 and q4 I still was in the ballpark of the questions just rounding differences also thanks for question 5. Also may I ask what your background knowledge is to be able to answer all of my questions Last edited by Posher; March 19th, 2017 at 09:11 PM.
March 20th, 2017, 07:43 AM   #6
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Quote:
 I'm pretty sure even though you got slightly different answers to me in q3 and q4 I still was in the ballpark of the questions just rounding differences
I don't round calculations until the very end ... a good habit to develop. One may avoid mid-step rounding by using the "store" feature of a calculator.

Quote:
 may I ask what your background knowledge is to be able to answer all of my questions
Taught advanced placement calculus and physics (mechanics) for about 20 years in a public high school.

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