How far is the football displaced from its original position?
A quarterback takes the ball from the line of scrimmage, runs backward for 10yards, then sideways parallel to the line of scrimmage for 15yards. he then throws a 50yard forward pass straight down-field perpendicular to the line of scrimmage. the receiver is tackled immediately.
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Lateral motion doesn't count on the football field. So in effect, this is a one-dimentional problem, with only forward and backward motion contribiuting to the displacement.
-10 + 50 yards = 40 yards total displacement.
a^2 + b^2 = c^2
a=15 b=40 c= x
Here's where you get these numbers.
From the starting point, draw a line down and label it 10. Then draw a slightly longer line to the right and label it 15. From here draw another still longer line up and label it 50. Make each length of these lines relative to the amount of the numbers.
Since the problem want to know the displacement of the ball from the scrimmage line, you will now draw a line from the starting point to the end point. Now draw another line from the starting point straight over to the right and end the line where it intersects the line representing 50. Your diagram should look like a rectangle with a triangle joined along the top side.
One side of your triangle with measure 15. The other known edge will measure 40. You need to find the measurement of the hypotenuse.
15 * 15= 225
40 * 40 = 1600
225 + 1600 = 1825
The square root of 1825 equals 42.72 when rounded to the nearest hundredth.
So the football was displaced approximately 42 feet. This is the distance from its starting point to the end point.
Let us say that the line of scrimmage runs east-west, and backward side is to the north and forward sise is to the south.
Then the quarterback first takes the ball 10 yards backward to the north.
Then the ball is taken 15 yards sideqways, let us say to the west.
When the ball is thrown 50 yards forward it travels in south direction.
At first 15 yards of the throw brings the ball crosses line of scrimmage at the point 15 yards east of the starting point.
on completing the throw of50 yards the ball is at a point which is, in relation to the starting point, 15 yards to the east and 35 yards to the south.
The distance between the starting point and the final point is the diagonal with length equal to
(15^2 + 35^)^(1/2) = (225 + 1225)^(1/2) = 1450^(1/2) = 38.089 yards (approximately)
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