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Earth's gravitational potential energy: [tex][tex]$G P E= mgh = \operatorname{Gravity}\left(9.81 \, m/s^2\right) \times$[/tex][/tex] Mass (kg) [tex] \times[/tex] Height (m)

Kinetic energy: [tex][tex]$K E=\frac{1}{2} m v^2$[/tex][/tex]

How would you calculate the kinetic energy of a [tex][tex]$0.148 \, kg$[/tex][/tex] ([tex][tex]$5.22 \, oz$[/tex][/tex]) baseball traveling at [tex][tex]$40 \, m/s$[/tex][/tex] ([tex][tex]$90 \, mph$[/tex][/tex])?

A. [tex][tex]$\frac{(0.148)(40)}{2}$[/tex][/tex]
B. [tex][tex]$\frac{(0.148)(40)}{9.8}$[/tex][/tex]
C. [tex][tex]$\frac{(0.148)(40)^2}{2}$[/tex][/tex]
D. [tex][tex]$(0.148)(40) \times 9.8$[/tex][/tex]

Sagot :

GinnyAnswer
To find the kinetic energy of a [tex]$0.148$[/tex] kg baseball traveling at [tex]$40$[/tex] m/s, we can use the formula for kinetic energy, which is given by:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]

Let's break down the step-by-step solution:

1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = [tex]$0.148$[/tex] kg
- Velocity ([tex]\( v \)[/tex]) = [tex]$40$[/tex] m/s

2. Substitute the given values into the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} \times 0.148 \times (40)^2 \][/tex]

3. Calculate the value inside the parentheses first:
[tex]\[ (40)^2 = 1600 \][/tex]

4. Then multiply by the mass:
[tex]\[ 0.148 \times 1600 = 236.8 \][/tex]

5. Finally, multiply by [tex]$\frac{1}{2}$[/tex]:
[tex]\[ KE = \frac{1}{2} \times 236.8 = 118.4 \][/tex]

Therefore, the kinetic energy of the baseball is approximately [tex]$118.4$[/tex] Joules.

Given the options:
A. [tex]\(\frac{(0.148)(40)}{2}\)[/tex]
B. [tex]\(\frac{(0.148)(40)}{9.8}\)[/tex]
C. [tex]\(\frac{(0.148)(40)^2}{2}\)[/tex]
D. [tex]\((0.148)(40) \times 9.8\)[/tex]

The correct formula matches option C:
[tex]\[ \frac{(0.148)(40)^2}{2} \][/tex]

So, the answer is C.
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