physics question?

Question

The question is .....A high school kicker makes a 30.0 yd. field goal attempt (in american football) and hits the crossbar at a height of 10.0 ft. What is the net displacement of the football from the time it leaves the ground until it hits the crossbar? I'm so confused......please help!

Answer 1

Sounds like a simple right triangle equation, assuming the ball travels a straight line when kicked. Displacement is simply the moving of something from its place or position. So we need to calculate the actual distance the ball travels in the air.

So a^2 + b^2 = c^2

The horizontal distance along the ground from the ball to the crossbar (a) = 30 yds (or 90 ft, gotta keep untis of measurement the same). The vertical height from the ground up to the crossbar (b) = 10 ft. Solve for the diagonal distance c from the ball to the crossbar (that is the net displacement).

90^2 + 10^2 = c^2
8100 + 100 = c^2
8200 = c^2
Take the square root of 8200:
c = 90.6 ft.

Answer 2

net displacement is simply the distance between its end point and start point. surely the kicker doesn't kick the ball in a straight line to the crossbar, the ball will follow a parabolic path. if you know the path, you can perform a line integral to calculate the total distance traveled by the ball, but that's not what is asked.
we just need to find that straight line distance between end and start points. just use Pythagoras' theorem to calculate hypotenuse of the right triangle having one side 30 yd and other side 10 ft (or 10/3 yd).

sqrt(30^2 + (10/3)^2) = 30.18 yd

Answer 3

There is insufficient information to answer the question. The word displacement means the distance traveled. The path of the football would need to be sufficiently constrained by the details of the problem to have a single path or that all possible paths had the same length. There are an infinite number of parabolas that have the two points listed in common. In a like manner there are an infinite number of curved shapes that are similar to parabolas but which have been slightly adjusted to take into account air resistance. There must have been some additional details in the original problem description.

Answer 4

The net displacement is 30.18 yards. To solve this problem make a right triangle where 30 yds is the horizonal component, 3.33 yds(10 ft) is the vertical component. Then use pythagoreans theorem to figure out the hypotenuse which will be the displacement.

Answer 5

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