A 0.145-kg baseball pops straight up from the ground at 21.4 m/s(a) What maximum height does it reach? (b) Find the work done by gravity on the baseball during its upward flight. (c) Find the work done by gravity for the entire round trip, from launch to when the ball hits the ground.

(a) h = 23.34 m

(b) W = - 33.2 J

(c) W = 0 J

Explanation:

(a)

We will use the third equation of motion to find out the height reached by the ball:

where,

g = acceleration due to gravity = - 9.81 m/s² (-ve sign due to upward motion)

h = height reached by ball = ?

vf = final speed = 0 m/s

vi = initial speed = 21.4 m/s

Therefore,

h = 23.34 m

(b)

The work done by gravity on the ball will be equal to its potential energy:

W = mgh

where,

W = Work done = ?

m = mass of ball = 0.145 kg

Therefore,

W = (0.145 kg)(- 9.81 m/s²)(23.34 m)

W = - 33.2 J

(c)

The total work done will be the sum of the work done during upward and downward motion. Here the magnitude of the work done during upward motion will be the same as the magnitude of the work done during downward motion with opposite direction. Therefore,

W = -33.2 J + 33.2 J

W = 0 J

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 .