Jeremy stands in a boat and throws a 4.2 kg rock horizontally off the end of the boat. While the rock is in his hand, it accelerates horizontally at 20.2 m/s$^2$.

What is the magnitude of acceleration (in m/s$^2$) of Jeremy and the boat (assuming his feet are not sliding in the boat)? The combined mass of Jeremy and the boat is 94 kg.

The acceleration of Jeremy and the boat after the rock is thrown can be calculated by dividing the force exerted when throwing the rock (which is the rock's mass times its acceleration) by the combined mass of Jeremy and the boat.

Explanation:

From the principle of conservation of momentum, when Jeremy throws the rock, he and the boat will move in the opposite direction but with a much smaller acceleration, due to their larger combined mass. To calculate the acceleration, use the formula F = m * a (Force equals mass times acceleration), where the force exerted is the rock's mass times its acceleration: 4.2 kg * 20.2 m/s2. This force also acts on Jeremy and the boat but in the opposite direction, so the acceleration of Jeremy and the boat will be:

F / M (Force divided by the mass of Jeremy+boat). and this equals (4.2 kg * 20.2 m/s2) / 94 kg.

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