A kicker punts a football from the very center of the field to the sideline 39 yd downfield. What is the magnitude of the net displacement of the ball? (A football field is 55 yd wide.) What is the angle of the net displacement of the ball from a line down the center of the field?

tan theta = y/x = 27.5 / 39

theta = tan^-1 ( 0.705) = 35.2 degrees

x = 39

y = 55/2 = 27.5

d = sqrt [ 39^2 + 27.5^2 ]

tan theta = y/x = 27.5 / 39

I was able to figure out "What is the magnitude of the net displacement of the ball? "

It is 48 yd

I only need help with "What is the angle of the net displacement of the ball from a line down the center of the field?"

thanks

Well, let's put our punting skills to the test, shall we? The magnitude of the net displacement of the ball is simply the distance it covers from the center to the sideline, which in this case is 39 yards.

Now, as for the angle of the net displacement of the ball from a line down the center of the field, I'd like to imagine it going in a curve, twirling like a ballerina. But, alas, a football field is straight and boring. So, the angle would be a perfect 90 degrees, forming a right angle with the sideline.

But hey, if you think about it, that angle might be a bit off-center if you take the curvature of the Earth and the cosmic wind into account. So, let's just say the angle is "straight-ish" and leave it at that.

To find the magnitude of the net displacement of the ball, we can use the Pythagorean theorem. The net displacement is the hypotenuse of a right triangle formed by the horizontal and vertical displacements.

1. First, let's find the horizontal displacement. The football field is 55 yards wide, and the kicker punts the ball to the sideline, which is 39 yards downfield. So, the horizontal displacement is 55 yards.

2. Now, let's find the vertical displacement. Since the ball was punted from the very center of the field, there is no vertical displacement. So, the vertical displacement is 0 yards.

3. Now, we can calculate the magnitude of the net displacement using the Pythagorean theorem: the square of the hypotenuse (net displacement) is equal to the sum of the squares of the other two sides (horizontal and vertical displacements).

magnitude of net displacement = √(horizontal displacement^2 + vertical displacement^2)
magnitude of net displacement = √(55^2 + 0^2)
magnitude of net displacement = √3025
magnitude of net displacement ≈ 55 yards

Therefore, the magnitude of the net displacement of the ball is approximately 55 yards.

To find the angle of the net displacement of the ball from a line down the center of the field, we can use trigonometry.

4. The angle can be determined using the tangent function:

tangent(angle) = vertical displacement / horizontal displacement
tangent(angle) = 0 / 55 (since the vertical displacement is 0)
tangent(angle) = 0

Since the tangent of the angle is 0, the angle itself is 0 degrees.

Therefore, the angle of the net displacement of the ball from a line down the center of the field is 0 degrees.