a motorcycle is driven 50 km west then 30 km south and 25 km 30 degree west of south show the vector diagram find the total displacement of motorcycle
east components (x direction):
-50 -25 sin 30
= -50 -12.5
= -62.5
north components (y direction)
-30 - 25 cos 30
= -30 - 21.7
= -51.7
d = sqrt (62.5^2 + 51.7^2)
tan angle west of south = 62.5/51.7
an ant walks 22 cm in a northerly directions turns and walks southeasterly (45 degree East Of South) a distance of 47 cm what is a resultant displacement?
Hey, do it the same way.
i didn't gets how to solve
Alright, let's rev up our engines and break this down! 🏍️
First, the motorcycle is driven 50 km west. So we'll draw an arrow pointing to the left, representing this distance.
Next, the motorcycle is driven 30 km south. We'll draw an arrow pointing downwards, representing this distance.
Finally, we have the motorcycle driving 25 km at a 30-degree angle west of south. To draw this, imagine the motorcycle moving towards the lower left direction, making a little turn. We'll draw an arrow accordingly, angled at 30 degrees from the straight south direction.
Now, we can add up all the distances covered by the motorcycle by measuring the length of the displacement arrow from the starting point to the end point. And voila, that's the total displacement of the motorcycle!
Keep in mind that the vector diagram needs to be drawn to scale to get accurate measurements. So, get your pencils and protractors ready, and happy drawing! 🎨
To find the total displacement of the motorcycle, we can use vector addition to combine the individual displacements in terms of magnitude and direction.
Step 1: Draw a coordinate system with the origin representing the starting point of the motorcycle.
Step 2: Draw the first vector, representing the displacement of 50 km west. Since it is only in the west direction, there is no vertical component, so the vector is drawn horizontally to the left.
Step 3: Draw the second vector, representing the displacement of 30 km south. Since it is only in the south direction, there is no horizontal component, so the vector is drawn vertically downward.
Step 4: Draw the third vector, representing the displacement of 25 km 30 degrees west of south. To do this, draw a line in the south direction, then rotate it 30 degrees to the right (clockwise) from the vertical axis. The line should end slightly to the right and downward from the vertical vector drawn in step 3.
Step 5: Measure the lengths of the three vectors. Let's call them A, B, and C respectively. So, A = 50 km, B = 30 km, and C = 25 km.
Step 6: Now, draw the resultant vector by starting from the origin and drawing a vector that represents the sum of A, B, and C. Connect the starting point of A to the ending point of C. This represents the total displacement of the motorcycle.
Step 7: Measure the magnitude of the resultant vector. This can be done using a ruler or by calculating the geometric sum of A, B, and C.
Step 8: Use trigonometry to find the direction of the resultant vector. Calculate the angles between the resultant vector and the x-axis and between the resultant vector and the y-axis.
By following these steps, you will find the total displacement of the motorcycle, including both magnitude and direction.