A 322-kg boat is sailing 14.4° north of east at a speed of 1.86 m/s. Thirty seconds later, it is sailing 38.4° north of east at a speed of 3.72 m/s. During this time, three forces act on the boat:
To find the change in velocity and calculate the net force acting on the boat, we'll need to break down the given information step by step. Let's go through the process:
Step 1: Convert the velocities from polar coordinates to Cartesian coordinates.
The initial velocity is given as 14.4° north of east with a magnitude of 1.86 m/s. To convert this velocity vector to Cartesian coordinates (x, y), we can use trigonometry:
Vx = V * cos(θ)
Vy = V * sin(θ)
Where V is the magnitude of the velocity and θ is the angle with respect to the positive x-axis.
For the initial velocity:
V1x = 1.86 m/s * cos(14.4°)
V1y = 1.86 m/s * sin(14.4°)
Similarly, convert the second velocity (38.4° north of east with a magnitude of 3.72 m/s) to Cartesian coordinates:
V2x = 3.72 m/s * cos(38.4°)
V2y = 3.72 m/s * sin(38.4°)
Step 2: Calculate the change in velocity, Δv.
Δv = (V2x - V1x, V2y - V1y)
Δv = (V2x - V1x, V2y - V1y)
Step 3: Calculate the acceleration, a.
Since we know the time interval Δt (30 seconds), we can use the formula:
a = Δv / Δt
Step 4: Calculate the net force acting on the boat, F_net.
To calculate the net force, we use Newton's Second Law: F_net = m * a
Given the mass of the boat m = 322 kg, we can calculate:
F_net = 322 kg * a
By following these steps, we can find the answers.