Two soccer players kick a soccer ball back and forth along a straight line. The first player kicks the ball 19 m to the right to the second player. The second player kicks the ball to the left weakly; it only moves 1.7 m before stopping. (Consider the right to be the positive direction. Where applicable, indicate the direction with the sign of your answer.)
(a) What is the total distance that the ball moved?
(b) At the end, what is the displacement of the ball (from the first player)?
(a) 19 + 1.7
(b) 19 - 1.7
(a) Well, it seems like the ball is quite indecisive. First, it moves 19 meters to the right, then only 1.7 meters to the left. So, to find the total distance, let's add those up: 19 + 1.7 = 20.7 meters. That's the total distance the poor ball had to endure.
(b) Now, let's talk about the displacement. The first player kicked the ball 19 meters to the right, and the second player kicked it 1.7 meters to the left. So, to find the displacement, we need to consider the direction as well.
Since the right direction is considered positive, we can say that the first player's kick had a positive displacement of 19 meters. And since the second player's kick was in the left direction, we'll consider it as a negative displacement of 1.7 meters.
To find the overall displacement, we just need to add those up: 19 - 1.7 = 17.3 meters to the right. So, at the end, the ball was displaced 17.3 meters to the right from the first player.
To solve this problem, we need to calculate the total distance that the ball moved and the displacement of the ball.
(a) To find the total distance, we need to add up the distances moved by the ball in each kick. The first player kicks the ball 19 m to the right, and the second player kicks it 1.7 m to the left.
Total distance = distance kicked by the first player + distance kicked by the second player
= 19 m + 1.7 m
= 20.7 m
Therefore, the total distance that the ball moved is 20.7 meters.
(b) The displacement of an object is the straight-line distance between its initial position and its final position. In this case, the initial position of the ball is at the first player. The first player kicks the ball to the right, and the second player kicks it to the left.
Since the second player kicked the ball weakly and it only moved 1.7 m to the left, the displacement of the ball is the difference between the distance moved to the right by the first player and the distance moved to the left by the second player.
Displacement = distance kicked by the first player - distance kicked by the second player
= 19 m - 1.7 m
= 17.3 m to the right
Therefore, the displacement of the ball from the first player is 17.3 meters to the right.
To find the total distance that the ball moved, we need to add up the distances traveled by each player.
The first player kicks the ball 19 m to the right, so the distance traveled by the ball is 19 m.
The second player kicks the ball 1.7 m to the left. Since we are considering the right as the positive direction, we can consider this as a negative displacement of 1.7 m.
To find the total distance, we add the absolute values of the distances traveled by each player.
Total distance = |19 m| + |-1.7 m| = 19 m + 1.7 m = 20.7 m
Therefore, the total distance that the ball moved is 20.7 m.
To find the displacement of the ball at the end, we need to find the net distance traveled and the direction.
The first player kicked the ball 19 m to the right, and the second player kicked the ball 1.7 m to the left. So, the net distance traveled is 19 m - 1.7 m = 17.3 m (to the right).
Therefore, the displacement of the ball from the first player is 17.3 m to the right.