a baseball has a mass of 0.145 kg and is 12 m above the ground. if it has a mechanical energy of 105.8 j…

Explanation:

Step1: Identify mechanical - energy formula

Mechanical energy $E = K+U$, where $K=\frac{1}{2}mv^{2}$ (kinetic energy) and $U = mgh$ (potential energy), $m = 0.145$ kg, $h = 12$ m, $g=9.8$ m/s², $E = 105.8$ J.

Step2: Calculate potential energy

$U=mgh=0.145\times9.8\times12$ $U = 0.145\times117.6=17.052$ J.

Step3: Calculate kinetic energy

$K=E - U$. $K=105.8 - 17.052 = 88.748$ J.

Step4: Solve for velocity

Since $K=\frac{1}{2}mv^{2}$, then $v=\sqrt{\frac{2K}{m}}$. $v=\sqrt{\frac{2\times88.748}{0.145}}=\sqrt{\frac{177.496}{0.145}}=\sqrt{1224.11}$ $v\approx35$ m/s.

Answer:

35 m/s