Question

Two people pull as hard as they can on horizontal ropes attached to a boat that has a mass of 200 kg. If they pull in the same direction, the boat has an acceleration of 1.42 m/s2 to the right. If they pull in opposite directions, the boat has an acceleration of 0.509 m/s2 to the left. What is the magnitude of the force each person exerts on the boat

Answer 1

Answer: 192.9N and 91.1N

Step-by-step explanation:

Let the force exerted by one person = X

Let the force exerted by the other person = y

Then, we can create equations

When both persons pull in the same direction, then

X + Y = 200 * 1.42

When both persons pull I'm opposite directions, then

X - Y = 200 * 0.509

Now we have

X + Y = 284

X - Y = 101.8

When we add the 2 equations together, we get

2X = 385.8

X = 385.8/2

X = 192.9

If x = 192.9, then, y = 284 - x

Y = 91.1

Therefore, one person exerts 192.9N, and the other exerts 91.1N