Question

Suppose that a pitcher can throw a ball straight up at$100mi/h$

(about 45 m/s). Use energy conservation to calculate how high the baseball goes, Explain your work. Actually, a pitcher can’t attain this high a speed when throwing straight up, so your result will be an overestimate of what a human can do; air resistance also reduces the achievable height

Short answer

The baseball goes 103.21 m in height

Step-by-step solution

Identification of Given Data

The speed of the baseball is$45m/s$

Significance of principle of energy conservation

The energy is produced or destroyed as per the conservation of energy principle. The principle says that the experimental observations depend on the cogency of the energy conservation.

According to the principle of energy conservation,

Loss of potential energy = Gain in kinetic energy

Calculation of the height goes by the baseball

To find the height goes by the baseball, we have to apply Principle of energy conservation,

$h=\frac{v^2}{2g}.........\left(1\right)$

Where,

$$\begin{gathered} h=heightgoesbybaseball \\ v=speedoftheball\Rightarrow 45m/s \\ g=accelerationduetogravity\Rightarrow 9.81m/s \end{gathered}$$

Substitute the values in Equation,

$$\begin{gathered} h=\frac{{45}^2}{2\times 9.81} \\ h=103.21m \end{gathered}$$

Hence, the baseball goes103.21 mheight.

• If we throw a baseballstraight up, it will experience deacceleration due to gravity.
• When a baseball reaches maximum height, the kinetic energy will be zero.
• The potential energy will become high.
• When the gravitational force starts accelerating, the kinetic energy will become high.