Question

Ann (mass 50 kg) is standing at the left end of a 15-m-long, 500 kg cart that has frictionless wheels and rolls on a frictionless track. Initially both Ann and the cart are at rest. Suddenly, Ann starts running along 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?
Express your answer with the appropriate units.

Answer 1

Answer:

13.5 m

Explanation:

M = Mass of cart = 500 kg

m = Ann's mass = 50 kg

$v_m$ = Velocity of Ann relative to cart = 5 m/s

$v_M$ = Velocity of Cart relative to Ann

As the linear momentum of the system is conserved

$Mv_M+mv_m=0\\\Rightarrow v_M=-\frac{mv_m}{M}\\\Rightarrow v_M=-\frac{50\times 5}{500}\\\Rightarrow v_M=-0.5\ m/s$

Time taken to reach the right end by Ann

$Time=\frac{Distance}{Speed}\\\Rightarrow Time=\frac{15}{5}=3\ s$

Distance the cart will move in the 3 seconds

$Distance=Speed\times Time\\\Rightarrow Distance=-0.5\times 3=-1.5\ m$

The negative sign indicates opposite direction

Movement of Ann will be the sum of the distances

$15+(-1.5)=13.5\ m$

The net movement of Ann is 13.5 m