Aball with a horizontal speed of 1.25m/s rolls off a bench 1.00m above the floor.

part a
how long will it take the ball to hit the floor?
part b
how far from a point on the floor directly below the edge of the bench will the ball land?

Part A: Time = 0.45 s

Part B: Horizontal distance = 0.5625 m

Explanation:

Part A:

       As the ball with a horizontal speed of 1.25 m/s rolls off a bench 1.00 m above the floor, it follow the projectile path.

Projectile motion is a two dimensional motion and the path followed by projectile motion is called projectile path.

Given data:

horizontal velocity = v₍ₓ₎ = 1.25 m/s

vertical velocity = v₍ₙ₎ = 0 m/s

Height = h = 1 m

From 2nd equation of motion

           h = v₍ₙ₎t + 0.5 gt²  

            1 = 0 + 0.5(9.81)t²

            2 = 9.81 t²

             t = √(0.2)

             t = 0.45 s

Part B:

        In projectile motion, horizontal component of velocity remain same,

So there is no acceleration in horizontal direction.

We can use the following formula

          Horizontal distance = R = v₍ₓ₎t

                                              R = 1.25 × 0.45

                                              R = 0.5625 m

cant without the picture! ?

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 .