Student on a cart?

A 63kg student stands on a 34kg cart that is free to move in any direction. The cart and student are moving together with a velocity of 3.2m/s [W]. The student then starts to walk so that her velocity is 1.8m/s [25° W of N] relative to the floor. Calculate the new velocity of the cart.

Student on a cart?
momentum is conserved in all directions





West:


(63+34)*3.2=63*1.8*cos25+


34*v*cos(theta)








North





0=63*1.8*sin25-34*v*sin(theta)





solve for v





(97*3.2-63*1.8*cos25)=34*v*cos(theta)


63*1.8*sin25=34*v*sin(theta)





divide


tan(theta)=63*1.8*sin25/


(97*3.2-63*1.8*cos25)





13 degrees





v=(97*3.2-63*1.8*cos25)/(34*cos13)


6.267 m/s





v=63*1.8*sin25/(34*sin13)


6.267 m/s





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