The most powerful tugboats in the world are built in Finland. Theseboats exert a force with a magnitude of 2.85 * 10^6N. Suppose one ofthese tugboats is trying to slow a huge barge that has a mass of 2.0 * 10^7kg and is moving with a speed of 3.0 m/s. If the tugboat exerts its maximum force for 21 s in the direction opposite to that in which thebarge is moving, what will be the change in the barge's momentum? Howfar will the barge travel before it is brought to a stop?

-5.985*10^7Ns=momentum

ds=31.578m

Explanation:

The most powerful tugboats in the world are built in Finland. Theseboats exert a force with a magnitude of 2.85 * 10^6N. Suppose one ofthese tugboats is trying to slow a huge barge that has a mass of 2.0 * 10^7kg and is moving with a speed of 3.0 m/s. If the tugboat exerts its maximum force for 21 s in the direction opposite to that in which thebarge is moving, what will be the change in the barge's momentum? Howfar will the barge travel before it is brought to a stop?

from newton's second law of motion, which states that the rate of change in momentum is directly proportional to the force applied

f=kdv/dt

k=1

ft=dv/dt

dp=dv/dt

f=negative because its moving in the opposite direction

2.85 * 10^6*21=

-5.985*10^7Ns=momentum

-dp=mv2-mv1

-dp+mv1=mv2

-5.985*10^7+2.0 * 10^7 kg*3.0 m/s=2.0 * 10^7kgV2

v2=150000 / (2.0 * 10^7)

v2=0.0075m/s to the right

ds=1/2 (v2+v1) dt

ds=0.5 * (3.0075) * 21

ds=31.578m

the barge will travel 31.578m before it is brought to rest.