A boat moves through the water with two
forces acting on it. One is a 2.32×10^3 N
forward push by the motor, and the other is a1.79×10^3 N resistive force due to the water.What is the acceleration of the 1279.5 kg boat?
2.32 - 1.79 = .53
so
F = ma
.53 * 10^3 = 1279.5 a
a = .414 m/s^2
By the way this is not really true because water is accelerated along with the boat hull, making its mass appear larger. In hydrodynamics this is often called "added mass"
thank you soo much damon
To find the acceleration of the boat, we can first calculate the net force acting on the boat using Newton's second law of motion, which states that the net force applied to an object is equal to its mass multiplied by its acceleration.
The net force is the vector sum of all the forces acting on the boat. In this case, the forward push by the motor creates a positive force, while the resistive force due to the water creates a negative force. Mathematically, we can express this as:
Net Force = Forward Push - Resistive Force
Given the values, the forward push is 2.32×10^3 N, and the resistive force is 1.79×10^3 N, so the net force is:
Net Force = 2.32×10^3 N - 1.79×10^3 N = 0.53×10^3 N
Now, we can calculate the acceleration using the formula:
Acceleration = Net Force / Mass
The mass of the boat is given as 1279.5 kg, so substituting the values into the equation, we get:
Acceleration = (0.53×10^3 N) / (1279.5 kg)
Calculating this yields the value of acceleration.
Note: It's important to convert the forces to the same units (e.g., Newtons) and ensure that the mass is in kilograms, as the standard metric units for force and mass are Newtons and kilograms, respectively.