An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a constant force of 220 N, toward east, on the boat. due to the angle of the sail, the wind causes the boat to slide in a staraight line for a distance of 8.5 m in a direction 20° north of east. What is the kinetic energy of the iceboat at the end of that 8.5 m?
To find the kinetic energy of the iceboat at the end of 8.5 m, we need to know its final velocity. We can calculate this using the given information about the force and distance.
First, let's break the force into its components. The force of 220 N can be split into two vectors: one along the east-west direction (x-axis) and one along the north-south direction (y-axis).
The force in the x-direction can be determined using trigonometry:
Fx = Force * cos(angle)
= 220 N * cos(20°)
The force in the y-direction can also be determined using trigonometry:
Fy = Force * sin(angle)
= 220 N * sin(20°)
Since there is no friction, the net force acting on the boat will be equal to its mass times acceleration:
Net Force = Mass * Acceleration
The mass cancels out when solving for acceleration:
Acceleration = Net Force / Mass
Since we know the force in both the x and y directions, we can calculate the net force acting on the boat using vector addition:
Net Force = √(Fx^2 + Fy^2)
Next, we can find the acceleration using the net force and the mass of the iceboat.
Finally, we can calculate the final velocity of the boat using the equation of motion:
vf^2 = vi^2 + 2aΔx
Since the boat starts from rest, the initial velocity (vi) is 0. Therefore, the equation simplifies to:
vf^2 = 2aΔx
Once we know the final velocity, we can calculate the kinetic energy using the equation:
Kinetic Energy = 0.5 * Mass * Velocity^2