two cars start moving from the same location but in different ways, then angle between them is 125. The first car moves 60 mph and the second car moves 75 mph how far apart are they after 2 hours and 45 mins?
For the given times,
one car went 2.75(60) miles or 165 miles
and the other 2.75(75) or 206.25 miles
d^2 = 165^2 + 206.25^2 - 2(165)(206.25)cos125°
= 108803.1087
d = √..
= 329.85 miles
Thank you this helped so much!
To find the distance between two cars after a certain amount of time, we can use the concept of relative velocity.
First, let's convert the given time of 2 hours and 45 minutes into hours. Since there are 60 minutes in an hour, 45 minutes is equal to 45/60 = 0.75 hours.
Now, let's imagine the two cars have traveled for this time and determine how far they have moved.
For the first car, which is moving at 60 mph, the distance it has traveled can be found by multiplying its speed by time:
Distance of the first car = 60 mph * (2.75 hours) = 165 miles
Similarly, for the second car, which is moving at 75 mph:
Distance of the second car = 75 mph * (2.75 hours) = 206.25 miles
Now, we can find the distance between the two cars using trigonometry.
Since the angle between the two paths is 125 degrees, the distance between the two cars will be the side opposite to this angle in the triangle they form.
To find this distance, we can use the formula:
Distance between cars = sin(angle) * distance of the first car
Distance between cars = sin(125 degrees) * 165 miles
Calculating sin(125 degrees) yields approximately 0.819
Distance between cars = 0.819 * 165 miles
Therefore, the estimated distance between the two cars after 2 hours and 45 minutes is 134.935 miles.