a runner jops 12km north then turns and runs 16km east in three hours.a/what his displacement b/calculate his average speed c/calculate his average velocity/including the direction
12m
if x i is east and y j is north,
displacement = 16,000 meters i + 12,000 meters j
distance (what you maybe meant to say) = 1000sqrt(16^2+12^2) = 20,000 meters = 20 km
speed = 20 km meters / 3 hours = 6.67 km/hr or 6.67 * 1000/3600 = 1.85 m/s
direction east of north = tan^-1 (16/12) = 53.1 deg east of north on compass = 36.9 deg North of east on math axes
sorry
displacement = 20 km
distance = 16 + 20 = 36 km
To calculate the runner's displacement, you'll need to find the straight-line distance from their starting point to their ending point. Here's how to do it:
a. Displacement:
1. Start by drawing a diagram to visualize the runner's movements. Take a point of reference as the starting point.
2. From the starting point, draw a line 12km in the north direction.
3. Then, from the end of the North line, draw a line 16km in the east direction.
4. Connecting the starting point with the ending point will give you a right-angled triangle.
5. Use the Pythagorean theorem (a^2 + b^2 = c^2) to find the displacement. In this case, the legs of the right-angled triangle are 12km and 16km, and the hypotenuse (displacement) will be the straight-line distance.
Displacement = √(12^2 + 16^2) km
b. To calculate the average speed, divide the total distance traveled by the total time taken:
Average Speed = Total Distance / Total Time
= (12km + 16km) / 3 hours
c. To calculate the average velocity, you'll need to consider both the magnitude (speed) and direction. The magnitude was calculated in part b, and now you need to determine the direction.
1. Calculate the north-south component of displacement by taking the vertical distance traveled (leg of the right-angled triangle). In this case, it is 12km.
2. Calculate the east-west component of displacement by taking the horizontal distance traveled (the other leg of the right-angled triangle). In this case, it is 16km.
3. Average Velocity = Displacement / Total Time
= (north-south component / 3 hours) i + (east-west component / 3 hours) j
Here, "i" represents the north-south direction, and "j" represents the east-west direction.
Remember to include the directions (north, east, etc.) in your final answers.