PLEASE ANSWER ASAP!!!!!!!!!!!!!!!!!!!!!!!
a cross country runner runs 3km due east, 5km due south and 8km south west. what is the runners final displacement?
change 8km SW to S and W components.
S=8cos45
W=8sin45
Net East= 3-8sin45
Net S=8cos45
Now add this to 5km S
displacement= s(5km+8Cos45)+ E(3-8sin45)
figure that out.
46.30
To find the final displacement of the runner, we need to calculate the net displacement by considering the distance traveled and the direction.
Step 1: Start by drawing a diagram to visualize the situation.
Draw a coordinate grid where the east direction is positive x-axis and the north direction is the positive y-axis. Mark the initial position of the runner as the origin (0, 0).
Step 2: Calculate the displacement in each direction.
The runner travels 3 km due east, so the displacement in the x-axis would be +3 km.
The runner then travels 5 km due south, so the displacement in the y-axis would be -5 km.
Finally, the runner travels 8 km southwest. This means the runner is moving in a direction 45 degrees southwest from the south direction. To calculate the displacement in the x and y directions, we need to find the horizontal and vertical components of the displacement.
The horizontal component = 8 km * cos(45°)
The vertical component = 8 km * sin(45°)
Step 3: Determine the overall displacement.
To find the overall displacement, we need to add up the displacements in each direction. Since the horizontal component is southwest, it is negative in the x-axis, and the vertical component is south, it is negative in the y-axis.
Overall displacement in the x-axis = +3 km - horizontal component
Overall displacement in the y-axis = -5 km - vertical component
Step 4: Calculate the magnitude and direction of the final displacement.
To find the magnitude of the final displacement, we can use the Pythagorean theorem.
Magnitude = √[(overall displacement in x-axis)² + (overall displacement in y-axis)²]
To find the direction of the final displacement, we can use the inverse tangent function.
Direction = arctan[(overall displacement in y-axis) / (overall displacement in x-axis)]
By following these steps and performing the calculations, you can find the runner's final displacement.