a car travels 59.78 miles east in 89.67 minutes, then 89.67 miles north in 59.78 minutes, and then 29.89 miles at 59.78 degrees west of south in 149.45 minutes. whats the magnitude of the car's average velocity in miles per hour???

Please help!!!!!!

P.S. please don't round your numbers till the final answer, so there are no rounding errors, and please round the final number to 4 significant figures.

Solve each leg as distance (vector displacement). Then add them as vectors.

Find then the final displacement.
avg velocity= finaldisplacemen/totaltime.

To find the magnitude of the car's average velocity, we first need to calculate the total displacement of the car.

First, let's break down the given information into separate components:

- The car travels 59.78 miles east in 89.67 minutes.
- The car travels 89.67 miles north in 59.78 minutes.
- The car travels 29.89 miles at 59.78 degrees west of south in 149.45 minutes.

Next, we can calculate the displacements along the x and y axes separately.

For the x (east-west) direction:
- The car moves 59.78 miles east, so the x-component of its displacement is +59.78 miles.

For the y (north-south) direction:
- The car moves 89.67 miles north and then goes 29.89 miles at a 59.78-degree angle west of south. To calculate the y-component, we can consider both distances as movements along the y-axis, with the northward distance being positive and the southward distance being negative. The westward distance will also be negative since it is in the opposite direction of the positive y-axis.
- The y-component of displacement = 89.67 miles - 29.89 miles * sin(59.78°) = 89.67 miles - 24.85 miles = +64.82 miles.

Now that we have calculated the x and y components of displacement, we can find the total displacement (d) using the Pythagorean theorem:

d = √(x^2 + y^2)
= √(59.78^2 + 64.82^2)
= √(3,573.28 + 4,207.92)
= √(7,781.2)
= 88.16 miles (to 4 significant figures)

The total displacement gives us the magnitude of the car's average velocity. However, the given times are in minutes, not hours. So, we need to convert the total displacement to miles per hour.

To convert from minutes to hours, we divide the total time by 60:

Total time = 89.67 minutes + 59.78 minutes + 149.45 minutes
= 298.9 minutes

Total time in hours = 298.9 minutes / 60
= 4.9817 hours (to 4 significant figures)

Finally, we can calculate the magnitude of the car's average velocity:

Average velocity = Total displacement / Total time
= 88.16 miles / 4.9817 hours
= 17.691 miles per hour (to 4 significant figures)

Therefore, the magnitude of the car's average velocity is 17.691 miles per hour.