Answer :
The kinetic energy of a baseball with a mass of 146 g and a velocity of <23i, 23j, -14k> m/s is = 91.5 J
we need to use the formula: KE = [tex](1/2)mv^2[/tex], where m is the mass of the baseball and v is its velocity.
1. Convert the mass of the baseball from grams to kilograms: 146 g× (1 kg / 1000 g) = 0.146 kg
2. Find the magnitude of the velocity vector: [tex]\sqrt{(23^2) + (23^2) + (-14^2)[/tex] = [tex]\sqrt{(529 + 529 + 196)[/tex] =[tex]\sqrt{ (1254)[/tex] ≈ 35.38 m/s
3. Calculate the kinetic energy using the formula: KE = [tex](1/2)mv^2[/tex]
Now, we can plug in the values:
KE = (1/2) × 0.146 kg × [tex](35.38 m/s)^2[/tex] ≈ 91.5 J
So, the kinetic energy of the baseball is approximately 91.5 J.
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