Question

An athlete leaves one end of a pool of length l at t = 0 and arrives at the other end at time t1. she swims back and arrives at the starting position at time t2. if she is swimming initially in the positive x direction, determine her average velocities symbolically in the first half of the swim, the second half of the swim, and the round trip. (assume that time t2 is from the other end of the pool to the starting point. use any variable or symbol stated above as necessary. indicate the direction with the sign of your answer.)

Answer 1

To determine the athlete's average velocities in different legs of the swim, we need to calculate the total distance covered and the total time taken. The average velocity in the first half of the swim is l/t1, in the second half it is also l/t1, and for the round trip it is (2l)/(t1 + t2).

Step-by-step explanation:

To determine the athlete's average velocities, we first need to calculate the total distance covered and the total time taken for each leg of the swim. In the first half of the swim, the athlete covers a distance of l/2 in a time of t1/2, so the average velocity in the first half is (l/2)/(t1/2) = l/t1. In the second half of the swim, the athlete covers the same distance of l/2 in the same time of t1/2, so the average velocity in the second half is also l/t1. For the round trip, the total distance covered is l + l = 2l and the total time taken is t1 + t2. Therefore, the average velocity for the round trip is (2l)/(t1 + t2).

Answer 2

Average velocity is defined as

`v = (displacement)/(time)`

now we have

when she cross the pool in time t1

`v = (L)/(t_1)`

when she cross the pool back to starting position

`v = - (L)/(t_2)`

Here negative sign is for its return path direction which is reversed of its initial direction.

now for the round trip

displacement = 0

so v = 0