# Math Help - Baseball - kinetic energy

1. ## Baseball - kinetic energy

I can't even figure out where to begin. Here's the way the problem reads:

In this problem we calculate the work required for a pitcher to throw a 90-mi/h fastball by first considering kinetic energy.

The kinetic energy of an object of mass and velocity is given by .

Suppose an object of mass , moving in a straight line, is acted on by a force that depends on its position . According to Newton’s Second Law

where and denote the acceleration and velocity of the object.

(a) Show that the work done in moving the object from a position to a position is equal to the change in the object’s kinetic energy; that is show that

Where and are the velocities of the object at the positions and . Hint: By the Chain Rule,

(b) How many foot-pounds of work does it take to throw a baseball at a speed of 90 mi/h?

2. Originally Posted by ReneePatt
I can't even figure out where to begin. Here's the way the problem reads:

In this problem we calculate the work required for a pitcher to throw a 90-mi/h fastball by first considering kinetic energy.

The kinetic energy of an object of mass and velocity is given by .

Suppose an object of mass , moving in a straight line, is acted on by a force that depends on its position . According to Newton’s Second Law

where and denote the acceleration and velocity of the object.

(a) Show that the work done in moving the object from a position to a position is equal to the change in the object’s kinetic energy; that is show that

Where and are the velocities of the object at the positions and . Hint: By the Chain Rule,

(b) How many foot-pounds of work does it take to throw a baseball at a speed of 90 mi/h?

$F(s) = m \frac{dv}{dt}$

Now multiply both sides by $ds$.

$F(s) \, ds = m \frac{dv}{dt} ds$

Now, note that $\frac{dv}{dt}ds = \frac{ds}{dt} dv = v dv$

Hence

$F(s) \, ds = m v dv$

Not integrate both sides:

$\int_{s_1}^{s_2} F(s) ds = \int_{v_1}^{v_2} mvdv$

For part b), you are simply subbing numbers into the equation that you derive in part a).

3. ## So for part b - where do I sub in the number?

Originally Posted by Mush
For part b), you are simply subbing numbers into the equation that you derive in part a).
Where do I sub in the numbers for part b?
I don't understand. How do you find the foot-pounds of work to throw the ball at a speed of 90 mi/h?