A 214 kg boat is sinking in the ocean. The boat's weight is partially offset by the 790 N buoyant force of the water. What is the net acceleration of the boat?
weight of boat (in N)- buoyant force = m*a
To find the net acceleration of the boat, we need to consider the forces acting on it. There are two forces at play here: the weight of the boat and the buoyant force exerted by the water.
The weight of the boat is the force pulling it downward, given by the formula:
Weight = mass * acceleration due to gravity
In this case, the mass of the boat is 214 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the boat is:
Weight = 214 kg * 9.8 m/s^2 = 2097.2 N
The buoyant force exerted by the water is an upward force that partially offsets the weight of the boat. In this case, the buoyant force is given as 790 N.
To find the net acceleration, we need to calculate the difference between the two forces:
Net Force = Weight - Buoyant Force
Net Force = 2097.2 N - 790 N = 1307.2 N
Finally, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Net Force = mass * acceleration
Rearranging the equation to solve for acceleration, we have:
acceleration = Net Force / mass
Plugging in the values, we get:
acceleration = 1307.2 N / 214 kg ≈ 6.1 m/s^2
Therefore, the net acceleration of the boat is approximately 6.1 m/s^2.