Two cars leave the same point at the same time, each travelling at the same constant speed of 89.0 km/h and each having the same mass. However, the first car drives directly east, while the second car heads directly south. At what speed (the magnitude of the velocity) is the centre of mass of these two cars travelling? Give your answer as a positive value in km/h (without a sign).
To find the speed at which the center of mass of the two cars is traveling, we need to use vector addition.
Since the first car is traveling directly east and the second car is traveling directly south, we can think of their velocities as vectors. The magnitude of their velocities is 89.0 km/h, but their directions are perpendicular to each other.
To find the resultant velocity, we can use the Pythagorean theorem. The resultant velocity is the vector sum of the two velocities, and it represents the velocity of the center of mass.
Using the Pythagorean theorem:
resultant velocity^2 = (velocity of the first car^2) + (velocity of the second car^2)
resultant velocity^2 = (89.0 km/h)^2 + (89.0 km/h)^2
resultant velocity^2 = 2(89.0 km/h)^2
resultant velocity = sqrt(2) * 89.0 km/h
Calculating this, we find that the resultant velocity is approximately 125.96 km/h.
Therefore, the speed at which the center of mass is traveling is approximately 125.96 km/h.
To find the speed at which the center of mass of the two cars is traveling, we can use the concept of vector addition.
Since the first car is traveling directly east and the second car is traveling directly south, their velocities can be represented as vectors in the x and y directions respectively.
The magnitude of the velocity of an object moving in two dimensions (x and y) can be found using the Pythagorean theorem.
Given that both cars have the same constant speed of 89.0 km/h, the magnitude of their velocities (v) will also be the same.
Using the Pythagorean theorem, we can find the magnitude of the velocity of the center of mass (V_cm) by summing the squares of the velocities in the x and y directions, and taking the square root.
V_cm = √(v^2 + v^2)
V_cm = √(89.0^2 + 89.0^2)
V_cm = √(7921 + 7921)
V_cm = √15842
V_cm ≈ 125.9 km/h
Therefore, the center of mass of the two cars is traveling at a speed of approximately 125.9 km/h.