3.3 Example 3

Two cars start from the same place. One with a constant velocity of 80 km/h at 50 degrees from the east, in the direction north-east. The other with a constant velocity of 95 km/h to the east. In what moment the distance between these cars is 50 km? Give your answer in minutes.

Solution with FisicaLab

Select the Kinematic group and, inside this, the Particles module. Erase the content of the chalkboard. And add one element Mobile in X whit constant velocity, one element Mobile radial, one element Distance and one element Stationary reference system. As show the image below:

The end time, is an unknown data, then in the element Stationary reference system write:

tf

t @ min

Because we want the time in minutes. Now, we assume that both cars start from the origin of the stationary reference system, and at the time 0. Then, to the element Mobile radial write, we call this car Car 1:

Name

Car 1

a

0

angf

50

xi

0

yi

0

vi

88 @ km/h

ti

0

xf

xf1

yf

yf1

vf

vf1

We write the final velocity as an unknown data. Although, the acceleration is 0. We do this to satisfied numbers of equations = numbers of unknown data. Now, to the Mobile in X write, we call this Car 2:

Name

Car 2

xi

0

xf

xf2

ti

0

vx

95 @ km/h

To the element Distance:

Object 1

Car 1

Object 2

Car 2

d

50 @ km

Where Object 1 and Object 2 are, respectively, the Car 1 and Car 2. And d is the distance between both cars, in this case 50 kilometers.

Now click in the icon Solve to get the answer.

xf1 = 36447.231 m ;  yf1 = 43436.119 m ;
vf1 = 24.444 m/s ;  t = 38.660 min ;
xf2 = 61212.198 m ;
Status = success.

The desired data is t = 38.660 min.