Question

1. a 0.30 kg soccer ball is released from the top of a 10 m building. the ball strikes the ground with a speed of 12 m/s. use the conservation of energy to determine the energy lost due to the work done by air resistance. a. 29.4 j b. 21.6 j c. 27.6 j d. 7.8 j

Explanation:

Step1: Calculate initial potential energy

The initial potential energy \(U = mgh\), where \(m = 0.30\space kg\), \(g= 9.8\space m/s^{2}\), \(h = 10\space m\).
\(U=0.30\times9.8\times10=29.4\space J\)

Step2: Calculate final kinetic energy

The final kinetic energy \(K=\frac{1}{2}mv^{2}\), where \(m = 0.30\space kg\), \(v = 12\space m/s\).
\(K=\frac{1}{2}\times0.30\times12^{2}=\frac{1}{2}\times0.30\times144 = 21.6\space J\)

Step3: Calculate energy lost

By conservation of energy \(E_{lost}=U - K\)
\(E_{lost}=29.4 - 21.6=7.8\space J\)

Answer:

D. \(7.8\space J\)