Sure, let's break down the problem step-by-step to calculate the speed and velocity of the man moving 45 meters to the north and then 36 meters to the south in 27 seconds.
### Step 1: Understand the given information
We are given:
- Distance moved to the north: 45 meters
- Distance moved to the south: 36 meters
- Total time taken: 27 seconds
### Step 2: Calculate the total distance traveled
The total distance traveled by the man is the sum of the distances he moved in each direction:
Total Distance Traveled = Distance north + Distance south
[tex]\[
= 45 \, \text{meters} + 36 \, \text{meters}
= 81 \, \text{meters}
\][/tex]
### Step 3: Calculate the displacement
Displacement is a vector quantity, which means it has both magnitude and direction. Here, we consider the net effect of the man's movement in one direction. Since the man moves north and then south, the displacement will be the difference between these two movements.
Displacement = Distance north - Distance south
[tex]\[
= 45 \, \text{meters} - 36 \, \text{meters}
= 9 \, \text{meters \, north}
\][/tex]
### Step 4: Calculate the speed
Speed is a scalar quantity and is defined as the total distance traveled divided by the total time taken.
Speed [tex]\( = \frac{\text{Total Distance Traveled}}{\text{Total Time Taken}} \)[/tex]
[tex]\[
= \frac{81 \, \text{meters}}{27 \, \text{seconds}}
= 3.0 \, \text{meters per second}
\][/tex]
### Step 5: Calculate the velocity
Velocity is a vector quantity and is defined as the displacement divided by the total time taken.
Velocity [tex]\( = \frac{\text{Displacement}}{\text{Total Time Taken}} \)[/tex]
[tex]\[
= \frac{9 \, \text{meters}}{27 \, \text{seconds}}
= 0.3333 \, \text{meters per second \, north}
\][/tex]
### Summary of Results
- Total Distance Traveled: [tex]\( 81 \, \text{meters} \)[/tex]
- Displacement: [tex]\( 9 \, \text{meters \, north} \)[/tex]
- Speed: [tex]\( 3.0 \, \text{meters per second} \)[/tex]
- Velocity: [tex]\( 0.3333 \, \text{meters per second \, north} \)[/tex]
This is how you calculate the speed and velocity of the man's movement based on the provided distances and time.
