1.8 A jogger takes the following route to the entrance of their local park: north 45 m, west 60 m, south 75 m, and finally west 50 m. It takes them 7 minutes 26 seconds to reach the park entrance. (b) What is the average speed of the jogger?
45m[90o] + 60m[180o] + 75m[270o] + 50m[0o].
X = -60 + 50 = -10 m.
Y = 45 -75 = -30 m.
d^2 = (-10)^2 + (-30)^2 = 1000
d = 31.62 m.
Speed=d/t = 31.62m/7.433min.=4.25 m/min
To find the average speed of the jogger, we need to calculate the total distance traveled and divide it by the total time taken.
The total distance traveled is the sum of the distances traveled in each direction: north, west, south, and west again.
Distance traveled north = 45 m
Distance traveled west = 60 m + 50 m = 110 m
Distance traveled south = 75 m
Total distance traveled = 45 m + 110 m + 75 m = 230 m
The total time taken to reach the park entrance is given as 7 minutes 26 seconds, which can be converted to seconds as:
7 minutes = 7 * 60 = 420 seconds
26 seconds = 26 seconds
Total time taken = 420 seconds + 26 seconds = 446 seconds
Now, we can calculate the average speed of the jogger by dividing the total distance traveled by the total time taken.
Average speed = Total Distance / Total Time
= 230 m / 446 seconds
Calculating the average speed:
Average speed ≈ 0.516 m/s (rounded to three decimal places)
Therefore, the average speed of the jogger is approximately 0.516 m/s.
To calculate the average speed of the jogger, we need to divide the total distance traveled by the total time taken.
First, let's calculate the total distance:
The jogger traveled north 45 meters, then west 60 meters, then south 75 meters, and finally west 50 meters. To find the total distance, we'll add up these individual distances:
45 m + 60 m + 75 m + 50 m = 230 m
So, the total distance traveled by the jogger is 230 meters.
Now let's calculate the total time taken:
The jogger took 7 minutes 26 seconds to reach the park entrance. To calculate the total time in minutes, we'll convert the seconds to minutes by dividing it by 60:
7 minutes + (26 seconds / 60) minutes = 7.43 minutes
So, the total time taken by the jogger is 7.43 minutes.
Now, let's calculate the average speed:
Average Speed = Total Distance / Total Time
Average Speed = 230 m / 7.43 min
Before we can compute the average speed, we should convert the time from minutes to seconds, to ensure that the units are consistent. There are 60 seconds in a minute, so:
7.43 minutes * 60 seconds/minute = 446 seconds
Average Speed = 230 m / 446 s ≈ 0.516 m/s
Therefore, the average speed of the jogger is approximately 0.516 meters per second.