On the way to class, you walk north and then west such that your resultant displacement is 290 m in a direction 25deg west of north. Your average velocity is 2.0 m/s in the same direction as the displacement.

Calculate (a) your walking time and (b) your average speed.

Magnitude of displacement (vector)

=290m
velocity=2.0m/s

(a)
Walking time = distance /speed
= 290m / 2.0m/s
= 145s

(b)
Northerly distance
= 290cos(25°)
= 262.8m
Westerly distance
= 290sin(25°)
= 122.6m
Total distance
= 385.4m
Average speed
= 385.4m / 145s
= 2.66 m/s

Well, it seems like you took a bit of a detour on your way to class! Let's crunch some numbers and find out how long your comedic journey took!

(a) To find the walking time, we need to use the formula: time = distance / velocity.

The distance you covered is given as 290 m, and your velocity is 2.0 m/s. So, by plugging in these values, we get:

time = 290 m / 2.0 m/s = 145 s.

Therefore, your walking time (or should I say comedic stroll time) is 145 seconds.

(b) Now, to calculate your average speed, we simply divide the total distance traveled by the total time taken. Since the distance is still 290 m and the time is 145 s, we get:

speed = distance / time = 290 m / 145 s = 2 m/s.

So, your average speed is a steady 2 meters per second. It seems like you might have been on a roll with your comedic timing during this hilarious journey to class!

To solve this problem, we can use the formula:

Displacement = Velocity * Time

We are given the displacement as 290 m in a direction 25 degrees west of north and the average velocity as 2.0 m/s in the same direction as the displacement.

(a) To find the walking time:
We can calculate the time using the formula:

Time = Displacement / Velocity

Substituting the given values:

Time = 290 m / 2.0 m/s = 145 seconds

Therefore, the walking time is 145 seconds.

(b) To find the average speed:
The average speed is the total distance travelled divided by the total time taken. Since the displacement is not equal to the distance travelled, we need to find the distance.

Using the Pythagorean theorem, we can find the distance:

Distance = sqrt((Displacement north)^2 + (Displacement west)^2)

Since the displacement is 290 m in a direction 25 degrees west of north, we can calculate the north and west components of the displacement:

Displacement north = 290 m * cos(25 degrees)
Displacement west = 290 m * sin(25 degrees)

Substituting the values:

Displacement north = 290 m * cos(25 degrees) = 261.791 m
Displacement west = 290 m * sin(25 degrees) = 122.084 m

Using the Pythagorean theorem:

Distance = sqrt((261.791 m)^2 + (122.084 m)^2) = 290.094 m

Average Speed = Distance / Time

Substituting the values:

Average Speed = 290.094 m / 145 s = 2.001 m/s

Therefore, the average speed is approximately 2.001 m/s.

To solve this problem, we need to use trigonometry and the equations of motion. Let's break it down step by step.

Step 1: Determine the components of the displacement vector.
The resultant displacement of 290 m in a direction 25 degrees west of north can be broken down into its north and west components. The north component can be calculated using sin(θ) = opposite/hypotenuse, where θ is the angle west of north and the hypotenuse is the displacement.

North Component = sin(25) * 290 m = 122.31 m (rounded to two decimal places)

The west component can be calculated using cos(θ) = adjacent/hypotenuse.

West Component = cos(25) * 290 m = 261.48 m (rounded to two decimal places)

Step 2: Calculate the walking time.
To find the walking time, we can use the equation: time = distance/velocity.

The distance walked is the magnitude of the displacement vector, which is the hypotenuse of the triangle formed by the north and west components. We can use the Pythagorean theorem to find it:

Distance = √(North Component^2 + West Component^2)
Distance = √(122.31^2 + 261.48^2) ≈ 290.47 m (rounded to two decimal places)

Time = Distance/Velocity = 290.47 m / 2.0 m/s ≈ 145.24 s (rounded to two decimal places)

Therefore, the walking time is approximately 145.24 seconds.

Step 3: Calculate the average speed.
Average speed is defined as the total distance traveled divided by the total time taken.

Total Distance = Distance = 290.47 m
Total Time = Time = 145.24 s

Average Speed = Total Distance / Total Time = 290.47 m / 145.24 s ≈ 2.00 m/s (rounded to two decimal places)

Therefore, the average speed is approximately 2.00 m/s.