Car is travelling at E50degN at 15m/s. It makes a sudden turn and is now travelling N10degW with a speed of 10m/s, find the change in velocity
To find the change in velocity, we need to determine the initial velocity and the final velocity, and then subtract the initial velocity from the final velocity.
First, let's break down the initial and final velocities into their horizontal (x-component) and vertical (y-component) directions.
Initial velocity (E50degN):
- Speed: 15 m/s
- Direction: 50 degrees north of east (clockwise from the positive x-axis)
- Horizontal component: velocity_x1 = velocity1 * cos(theta1)
velocity_x1 = 15 m/s * cos(50 degrees)
velocity_x1 ≈ 15 m/s * 0.6428 ≈ 9.642 m/s (rounded to three decimal places)
- Vertical component: velocity_y1 = velocity1 * sin(theta1)
velocity_y1 ≈ 15 m/s * sin(50 degrees)
velocity_y1 ≈ 15 m/s * 0.7660 ≈ 11.490 m/s (rounded to three decimal places)
Final velocity (N10degW):
- Speed: 10 m/s
- Direction: 10 degrees west of north (counter-clockwise from the positive y-axis)
- Horizontal component: velocity_x2 = velocity2 * cos(theta2)
velocity_x2 ≈ 10 m/s * cos(10 degrees)
velocity_x2 ≈ 10 m/s * 0.9848 ≈ 9.848 m/s (rounded to three decimal places)
- Vertical component: velocity_y2 = velocity2 * sin(theta2)
velocity_y2 ≈ 10 m/s * sin(10 degrees)
velocity_y2 ≈ 10 m/s * 0.1736 ≈ 1.736 m/s (rounded to three decimal places)
Now, we can find the change in velocity by subtracting the initial velocity components from the final velocity components:
Change in velocity (in the x-direction): ∆velocity_x = velocity_x2 - velocity_x1
∆velocity_x ≈ 9.848 m/s - 9.642 m/s ≈ 0.206 m/s (rounded to three decimal places)
Change in velocity (in the y-direction): ∆velocity_y = velocity_y2 - velocity_y1
∆velocity_y ≈ 1.736 m/s - 11.490 m/s ≈ -9.754 m/s (rounded to three decimal places)
Therefore, the change in velocity is approximately 0.206 m/s in the x-direction and -9.754 m/s in the y-direction.