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3 years ago

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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 frictionles

s 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.

1 answer:

ivanzaharov [21]3 years ago

5 0

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

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