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a girl is skipping stones across a lake. one of the stones accidentally ricochets off a toy boat that is initially at rest in the water (see the drawing). the 0.072-kg stone strikes the boat at a velocity of 13 m/s, 15° below due east, and ricochets off at a velocity of 11 m/s, 12° above due east. after being struck by the stone, the boat's velocity is 2.1 m/s, due east. what is the mass of the boat? assume the water offers no resistance to the boat's motion.

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Final answer:

The student's physics question is about calculating the mass of a boat after a stone skips off it, using the conservation of linear momentum. We use the known masses and velocities of the stone before and after the collision, as well as the velocity of the boat to set up equations for momentum conservation in both the east and north directions and solve for the boat's mass.

Step-by-step explanation:

The question involves a collision in physics, specifically the conservation of momentum. Since we are told to assume no resistance to the boat's motion, we can use conservation of linear momentum to find the mass of the boat.

To solve the problem, we first need to calculate the momentum of the skipping stone before and after the collision. Momentum is given by the product of mass and velocity. The components of the momentum in the east direction (x-axis) can be calculated using the cosine of the respective angles, and those in the north direction (y-axis), using the sine. Now, momentum conservation tells us that the total momentum before the collision must equal the total momentum after the collision.

Before the collision, the boat is at rest, so its initial momentum is zero. After the collision, the boat and the stone have momentum that can be added vectorially. With the given velocities and angles of the stone's motion, and the eastward velocity of the boat, we can set up two equations for the conservation of momentum in the east (x) and north (y) directions.

For the eastward (x) direction, the equation is:
mstone × vstone, initial x = mstone × vstone, final x + mboat × vboat

And for the northward (y) direction, since the velocity of the boat in the y direction is zero after collision, the equation simplifies to:
mstone × vstone, initial y = mstone × vstone, final y

By solving these equations simultaneously, we can find the mass of the boat. This is a common type of problem in high school level physics that deals with conservation principles and vector components of velocity.

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