Question 1. A car moves 26 km due east then 14 km due north. It then turns along a path running north-east with 15 km, then 17 km due west. If the time for the entire journey is 2 hrs, Find; (a) the car’s average speed in m/s (b) the car’s average velocity in km/h . SOLVE THIS USING RESOLUTION OF VECTOR. NOTE YOU ARE TO FIND THE ANGLE TOO
Not Eng 102.
To solve this question using the resolution of vectors, we'll break down each movement into its respective components and use the equations for average speed and average velocity.
Let's denote the east direction as positive x-axis and the north direction as positive y-axis.
1. Car moves 26 km due east:
This can be represented as a displacement vector D1 with its x-component, Dx1 = 26 km, and y-component, Dy1 = 0 km.
2. Car moves 14 km due north:
This can be represented as a displacement vector D2 with its x-component, Dx2 = 0 km, and y-component, Dy2 = 14 km.
3. Car turns along a path running northeast for 15 km:
To find the components, we'll use the right triangle formed. The x-component Dx3 can be found using the angle θ formed between the northeast direction and the positive x-axis: cos(θ) = Dx3 / 15 km. Rearranging the equation, Dx3 = 15 km * cos(θ). Similarly, the y-component Dy3 = 15 km * sin(θ).
4. Car moves 17 km due west:
This can be represented as a displacement vector D4 with its x-component, Dx4 = -17 km, and y-component, Dy4 = 0 km.
The total displacement vector D_total is the sum of all the individual displacement vectors:
D_total = D1 + D2 + D3 + D4.
D_total = (Dx1 + Dx2 + Dx3 + Dx4) i + (Dy1 + Dy2 + Dy3 + Dy4) j.
Next, we'll calculate the average speed and average velocity.
(a) Average Speed:
Average speed is defined as the total distance traveled divided by the total time taken.
The total distance can be found by adding the magnitudes of all displacement vectors:
|D1| + |D2| + |D3| + |D4| = 26 km + 14 km + √(Dx3^2 + Dy3^2) + 17 km.
The total time taken is given as 2 hours.
Average speed = Total distance / Total time.
(b) Average Velocity:
Average velocity is the total displacement divided by the total time taken.
Average velocity = D_total / Total time.
To find the angle formed by the northeast direction and the positive x-axis (θ), we can use the equation: tan(θ) = Dy3 / Dx3.
By following these steps, you can calculate (a) the car's average speed in m/s, (b) the car's average velocity in km/h, and (c) the angle formed by the northeast direction and the positive x-axis.