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.
Do you need the degrees to solve this problem?? Alos please, if you are so kind explain step by step as to how to solve this problem.
thank you
The best way to solve this type of problems is by a table of component vectors.
Let x- and y-axes represent east and north respectively.
Resolve each segment of the trip into the x- and y-components.
Add up vectorially the components, which is the resultant displacement.
If the displacement is (x,y), the magnitude is √(x²+y²).
Work in hours, i.e. minutes should be divide by 60.
Distance x-component y-component
59.78 59.78*cos(0) 59.78*sin(0)
89.67 89.67*cos(90) 89.67*sin(90)
29.89 29.89*cos(270-59.78) 29.89*sin(270-59.78)
--------------------------------------
sum x y
Find (x,y), and the magnitude of displacment is √(x²+y²)
Divide the magnitude of displacement by the time (in hours) will give you the average velocity in miles per hour.
Post your answer for verification if necessary.
i got 16.46 mi/hr. is that right??
To find the magnitude of the car's average velocity, we first need to calculate the total displacement of the car and the total time it took.
Step 1: Calculate the total displacement:
- The car traveled 59.78 miles east and then 89.67 miles north, which we can represent as a vector sum.
- To find the total displacement, we can add these two vectors using vector addition.
- The displacement in the east direction can be represented as (59.78, 0) since there is no displacement in the north direction.
- The displacement in the north direction can be represented as (0, 89.67) since there is no displacement in the east direction.
- Adding these two vectors, we get the total displacement as (59.78, 89.67).
Step 2: Calculate the total time:
- The car took 89.67 minutes to travel east and then 59.78 minutes to travel north, and finally 149.45 minutes to travel in the west of the south direction.
- To calculate the total time, we simply add these three time intervals: 89.67 + 59.78 + 149.45 = 298.9 minutes.
Step 3: Convert minutes to hours:
- To convert minutes to hours, divide the total time by 60: 298.9 / 60 = 4.9817 hours.
Step 4: Calculate the magnitude of the average velocity:
- The magnitude of the average velocity is defined as the total displacement divided by the total time.
- The magnitude of a vector can be found using the formula: magnitude = √(x^2 + y^2), where x and y are the components of the vector.
- In our case, the x-component of the total displacement is 59.78, and the y-component is 89.67.
- Substituting the values into the formula, the magnitude of the displacement is √(59.78^2 + 89.67^2).
Step 5: Convert the magnitude to miles per hour:
- To convert the magnitude from miles per minute to miles per hour, multiply it by 60: magnitude * 60.
Therefore, to find the magnitude of the car's average velocity in miles per hour, calculate √(59.78^2 + 89.67^2) times 60, where √ represents the square root function. Round the final answer to 4 significant figures.