Which of the following represent examples of the following situation: An object that starts at the origin at t=0 and at some time later its displacement from origin is zero but the velocity is not zero:
1)An object in a uniform circular motion around a circle passing through origin
2)A tennis ball thrown toward a wall and returning to the ground
3)A projectile thrown at an angle of 45 degrees and returning to the ground
4)A ball thrown straight up and returning to the ground
all of those are at the origin, so displacement is zero, and all have some velocity at the origin.
To determine which of the given situations represents an object starting at the origin at t=0 and having a displacement of zero at some later time while having a non-zero velocity, we can analyze each option:
1) An object in a uniform circular motion around a circle passing through the origin:
To understand the situation, we need to consider that in uniform circular motion, the object moves in a circular path with a constant speed. However, since the object starts at the origin and returns to the origin, its displacement from the origin is zero at some point. The velocity, however, is not zero because the object is continuously changing its direction of motion. Therefore, option 1 satisfies the given criteria.
2) A tennis ball thrown toward a wall and returning to the ground:
In this scenario, the object (tennis ball) is thrown toward a wall and returns to the ground. While its displacement from the origin might be zero at some point (when it is closest to the wall), the velocity is zero at that moment. So, option 2 does not satisfy the given criteria.
3) A projectile thrown at an angle of 45 degrees and returning to the ground:
In this case, the object (projectile) is thrown at an angle and returns to the ground. Similar to option 2, the displacement may momentarily be zero when it is closest to the ground, but the velocity is zero at that instant. Thus, option 3 does not fulfill the criteria.
4) A ball thrown straight up and returning to the ground:
In this scenario, the object (ball) is thrown straight up and returns to the ground. While its displacement from the origin could be zero at the highest point, the velocity is zero at that instant. Hence, option 4 does not fulfill the given criteria.
So, based on the analysis, option 1 (an object in a uniform circular motion around a circle passing through the origin) is the correct answer as it represents an object starting at the origin at t=0, having a displacement of zero at some later time, and a non-zero velocity.