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Answer :
Answer:
41.78 m/s
Explanation:
Momentum the defined as the product of mass and velocity of an object hence expressed as p=mv where p represent momentum, m is mass while v is velocity.
The law of conseevation of linear momentum states that the sum of the initial and final momentum should be equal. Therefore, in this case, MV=mu where M and m represent mass of 61, 000 kg and 730 respectively while v and u are their respective velocities.
Making u the subject then
[tex]u=\frac {MV}{m}[/tex]
Substituting 0.5 m/s for V, 61000 kg for M and 730 kg for m then the velocity will be
[tex]u=\frac {61000\times 0.5}{730}=
41.780821917808 m/s\\u\approx 41.78 m/s[/tex]
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Rewritten by : Barada
The compact electric vehicle must travel at approximately 41.78 m/s to have the same momentum as the Rocky Mountain Double big rig moving at 0.5 m/s.
To find the velocity at which a 730-kg compact electric vehicle must travel to have the same momentum as a 61,000-kg Rocky Mountain Double big rig traveling at 0.5 m/s, we need to use the concept of momentum.
Step-by-Step Solution
Calculate the momentum of the Rocky Mountain Double:
Momentum (p) is given by the formula: [tex]p = m \times v[/tex]
For the big rig, [tex]m = 61,000 kg[/tex] and [tex]v = 0.5 m/s[/tex]:
[tex]p_{\text{big rig}} = 61,000 kg \times 0.5 m/s = 30,500 kg.m/s[/tex]Set the momentum of the electric vehicle equal to the big rig's momentum:
Le t[tex]v_{ev}[/tex] be the velocity of the electric vehicle (mass [tex]m_{ev}[/tex] = 730 kg). The required momentum is the same, so:
[tex]m_{ev} \times vev = 30,500 kg.m/s[/tex]Solve for the velocity of the electric vehicle:
[tex]v_{ev} = 30,500 kg.m/s / 730 kg = 41.78 m/s[/tex]
Thus, the compact electric vehicle must travel at approximately 41.78 m/s to achieve the same momentum as the Rocky Mountain Double big rig.
