A small utility car is pulled along a straight section of railroad tracks by a rope. When the ropepulls the car for 10 seconds the car reaches a final speed, after starting from rest, of 8m/s. Now the situation is modified slightly so that the rope pulls, just as hard as in the previous casebut at a 45 degree angle. After 10 seconds what would the final speed of the car be if we could ignore friction and other effects and why?

To find the final speed of the car when pulled at a 45-degree angle, we need to analyze the forces acting on the car and use vector addition to determine its acceleration.

When the car is pulled along a straight section of railroad tracks, the only external force acting on it is the tension in the rope. In the first case, the rope pulls the car directly forward, resulting in unidirectional motion. In this case, we know that the final speed after 10 seconds is 8 m/s.

In the modified situation, where the rope is pulling at a 45-degree angle, the force can be split into two components: one along the direction of motion and another perpendicular to it. The component along the direction of motion will accelerate the car, while the perpendicular component is not effective in changing the car's speed.

To determine the effective force along the direction of motion, we need to calculate the vector components. The force along the direction of motion can be found by multiplying the tension in the rope by the cosine of the angle between the rope and the direction of motion.

F_along_motion = Tension * cos(45°)

Since the force perpendicular to the direction of motion does not contribute to the speed of the car:

F_perpendicular = Tension * sin(45°)

However, since the problem states that we can ignore friction and other effects, this perpendicular force will also not affect the car's motion.

Hence, the effective force along the direction of motion will be the same as in the previous case (directly pulling the car forward). Therefore, the final speed of the car, after 10 seconds, will remain 8 m/s in this modified scenario.

In conclusion, even when the rope pulls the car at a 45-degree angle, the final speed of the car after 10 seconds will still be 8 m/s if we can ignore friction and other effects.

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