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Suppose that a tennis ball is thrown horizontally towards a wall at an initial velocity of to the right. After striking the wall, the ball returns to the thrower at . Determine the change in velocity of the ball.
A quick sketch will help us understand the problem.
Remember that velocity is a vector. The change in the velocity of the ball is equal to the difference between the ball's initial and finalvelocities:
Since the ball moves along a straight line (i.e. left and right), we can use the algebraic technique of vector subtraction just discussed.
Choose the positive direction to be towards the wall. This means that the negative direction is away from the wall.
Thus, the change in velocity of the ball is:
Remember that in this case towards the wall means a positive velocity , so away from the wall means a negative velocity : away from the wall.
Remember that the technique of addition and subtraction just discussed can only be applied to vectors acting along a straight line. When vectors are not in a straight line, i.e. at an angle to each other, the following method can be used:
Simple geometric and trigonometric techniques can be used to find resultant vectors.
A man walks 40 m East, then 30 m North. Calculate the man's resultant displacement.
As before, the rough sketch looks as follows:
Note that the triangle formed by his separate displacement vectors and his resultant displacement vector is a right-angle triangle. We can thus use the Theorem of Pythagoras to determine the length of the resultant. Let represent the length of the resultant vector. Then:
Now we have the length of the resultant displacement vector but not yet its direction. To determine its direction we calculate the angle between the resultant displacement vector and East, by using simple trigonometry:
The resultant displacement is then 50 m at North of East.
This is exactly the same answer we arrived at after drawing a scale diagram!
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