Question

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, how fast is it moving?
17 m/s
35 m/s
80 m/s
130 m/s

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).

Step2: Calculate potential energy

Given \(m = 0.145\ kg\), \(g=9.8\ m/s^{2}\), \(h = 12\ m\). So \(U=mgh=0.145\times9.8\times12\)
\[U = 0.145\times117.6=17.052\ J\]

Step3: Calculate kinetic energy

Given \(E = 105.8\ J\), and \(E=K + U\). So \(K=E - U\)
\[K=105.8 - 17.052=88.748\ J\]

Step4: Solve for velocity

Since \(K=\frac{1}{2}mv^{2}\), then \(v=\sqrt{\frac{2K}{m}}\)
Substitute \(K = 88.748\ J\) and \(m = 0.145\ kg\)
\[v=\sqrt{\frac{2\times88.748}{0.145}}=\sqrt{\frac{177.496}{0.145}}=\sqrt{1224.11}\approx17\ m/s\]

Answer:

17 m/s