A team has been working to convert diesel-powered cars to run just as efficiently on used cooking oil! They want to compare the mileage and speed of their prototype with that of the diesel-powered car.
The prototype is 100 meters south of an intersection, while the diesel car is 100 meters east of the intersection. Both vehicles start moving at the same time. The prototype moves north, toward the intersection, and the diesel car moves east, away from the intersection. If the prototype is traveling at a velocity of 3 meters per second and the diesel car is traveling at 2 meters per second, what is the rate of change of the distance between the cars after four seconds?
not sure sorry
To find the rate of change of the distance between the cars after four seconds, we can use the concept of relative velocity.
Relative velocity is the velocity of an object in relation to another object. In this case, we want to calculate the rate of change of the distance between the prototype and the diesel car, so we need to find their relative velocity.
The prototype is moving north at a velocity of 3 meters per second, while the diesel car is moving east at a velocity of 2 meters per second. Since their velocities are perpendicular to each other, we can use the Pythagorean theorem to find their relative velocity.
The relative velocity can be calculated as follows:
relative velocity = √((prototype velocity)^2 + (diesel car velocity)^2)
Substituting the given values:
relative velocity = √((3 m/s)^2 + (2 m/s)^2)
relative velocity = √(9 m^2/s^2 + 4 m^2/s^2)
relative velocity = √(13 m^2/s^2)
relative velocity ≈ 3.61 m/s
Now that we have the relative velocity, we can calculate the rate of change of the distance between the cars. Since the cars are moving in different directions, the distance between them is decreasing.
The rate of change of the distance between the cars is equal to the magnitude of the relative velocity.
rate of change of distance = relative velocity
Therefore, the rate of change of the distance between the cars after four seconds is approximately 3.61 meters per second.