At what speed do a bicycle and its rider, with a combined mass of 100 kg, have the same momentum as a 1500 kg car traveling at 5.0 m/s?

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Accepted Answer

Hi everyone in this practice problem. We're being asked to calculate the velocity of a un cyclist with a total mass of 80 kg, including the unicycle itself. For the unicycling to peddle across a tight rope to equal the momentum of a Cheetah weighing 60 kg, sprinting at a speed of 15 m per second. So the options given for the velocity of the unicycling are a 10.82 m per seconds. B 8.31 m per second. C 12.41 m per second and d 11.25 m per second. So first, I'm going to list all the different information from the problem statement. So first, we have, I'm going to um use the subscript U To indicate the un cyclist and the subscript c for the Cheetah. So we were given first the mass of the unicycles which is MU to be 80 kg. And then from there, we were also given the mass of the Cheetah which is 60 kg. We are given the velocity of the Cheetah which is going to be 15 m/s. And what we are interested at is the velocity of the uni cyclist to give the momentum equal to the momentum of the Cheetah. So to find this, we need to actually equate the momentum of un cyclists and the momentum of the Cheetah and momentum is going to be P. So we want to recall that momentum P will be calculated by multiplying the mass of a system multiply that by the velocity of a system. So what we wanna do here is to equate the momentum of the un cyclists, P U to the momentum of the Cheetah BC. So the equation will then become M U multiplied by V U equals MC multiplied by V C or the mass of the unicycle is multiplied by the velocity of the un cyclist equals to the mass of the Cheah multiplied by the velocity of the Cheetah. So we are interested in finding the philosophy of the un cyclist. So V U will then equals two, we are going to rearrange our momentum equation so that we can find the philosophy of the unicycling. So the philosophy of the unicycling will equals to MC multiplied by V C. All of that divided by the mass of the unicycles itself, which is M U. Then we can actually substitute all of our given information McM is going to be 60 kg multiplied by PC, which is going to be 15 m/s. All of that is going to be divided by the mass of the un cyclist. MU which is going to be 80 kg. Calculating this, we will find that the velocity of our uni cyclist is then going to be 11.25 m/s, which will actually correspond to option D. So option D with the velocity of the un cyclist to be 11.25 m per second is going to be the velocity that will give the equal momentum to the Cheetahs momentum weighing at kg, sprinting at 15 m per second. So that will be all for this particular practice problem. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topic and they'll be all for this one. Thank you.

At what speed do a bicycle and its rider, with a combined mass of 100 kg, have the same momentum as a 1500 kg car traveling at 5.0 m/s?

Verified Solution

Key Concepts

Momentum

Mass

Velocity