A player kicks a football from ground level with a velocity of magnitude 27.0 m/s at an angle of 30° above the horizontal.
What is the horizontal distance the ball travels?
(hint: d= 1/2 at^2)

37.33m

Explanation:

To calculate the distance using d= 1/2 at², the time taken for this projectile object (ball) must be calculated.

Time of a projectile = 2u sinθ/ g

Where u = velocity = 27m/s

g = 9.8m/s²

θ = 30°

T = 2usinθ/ g

T = 2 × 27 × sin 30°/9.8

T = 54sin30°/9.8

T = 27/9.8

T = 2.755

T = 2.76s

If the time taken for the ball to move is 2.76s, the distance travelled is:

D = 1/2at²

D = 1/2 × 9.8 × 2.76²

D = 1/2 × 9.8 × 7.6176

D = 74.65248/2

D = 37.33m

The horizontal distance the ball travels is 37.33m

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .