- #1
harimakenji
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Homework Statement
A stationary car with 4 people in it has mass 100 kg. The mass of each of the person is 75 kg. They jump off the car with speed 2 ms-1 relative to the car. Calculate the speed of the car if
a. 4 people jump at once
b. They jump one by one each time
Homework Equations
momentum and kinematics maybe
The Attempt at a Solution
1 = people
2 = car
a) m1u1+m2u2 = m1v1+m2v2
0 = 4 x 75 x 2 - 100 x v2
v2 = 6 ms-1
b) 1st person jumps
0 = 75 x 2 - 325 x v2
v2 = 6/13 ms-1
2nd person jumps
the speed of 2nd person relative to the car = 2 + 6/13 = 32/13 ms-1
m1 u1 + m2 u2 = m1 v1 + m2 v2
0 - 325 x 6/13 = 75 x 32/13 - 250 x v2
v2 = 87/65 ms-1
3rd person jumps
the speed of 3rd person relative to the car = 2 + 87/65 = 217/65 ms-1
m1 u1 + m2 u2 = m1 v1 + m2 v2
0 - 250 x 87/65 = 75 x 217/65 - 175 x v2
v2 = 117/35 ms-1
4th person jumps
the speed of 4th person relative to the car = 2 + 117/35 = 187/35 ms-1
m1 u1 + m2 u2 = m1 v1 + m2 v2
0 - 175 x 117/35 = 75 x 187/35 - 100 x v2
v2 = 69/7 ms-1
the final speed of the car is 69/7 ms-1
I am not sure whether my answers are correct. Can someone please help checking my answers? Thank you very much