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Chapter 11: Q. 59 (page 290)

Ann (mass 50kg) is standing at the left end of a 15mlong, 500kgcart that has frictionless wheels and rolls on a frictionless track. Initially, both Ann and the cart are at rest. Suddenly, Ann starts running along with the cart at a speed of 5.0m/srelative to the cart. How far will Ann have run relative to the ground when she reaches the right end of the cart?

Short Answer

Expert verified

Ann will run 13.65mrelative to the ground when she reaches the right end of the cart

Step by step solution

01

Step 1. Given information

Mass of Ann, mAnn=50kg

Mass of cart, localid="1649425458630" mcart=500kg

Velocity of Ann along with cart,localid="1649425472662" role="math" vann+cart=5m/s

02

Step 2. Analayze and apply

Ann's velocity relative to ground is, vAnn,ground=vAnn,cartvcart=5m/s+vcart.

On applying conservation principle,

mAnnvAnn,ground+mcartvcart=050kg5m/s+vcart+500kgvcart=0⇒vcart=−0.45m/s.

Now Ann's velocity is,vAnnground=5m/s+-0.45m/s=4.55m/s

03

Step 3. Calculate

To figure out how far Ann will go in relation to the, we must first determine how long it will take. We have the following:

vAnn,cart=dcartt⇒t=3s

Now using the distance formula we have,dAnn=vAnn,groundt=13.65m

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