Question

a 10 - kg rock falls from a ledge that is 20 m high, and it accelerates at $-9.8\frac{m}{s^{2}}$. what are the potential and kinetic energy after it falls for 1.0 s, at which point it has fallen 4.9 m? neglect air resistance. (1 point)

the potential energy is 1,500 j and the kinetic energy is 480 j.

the potential energy is 1,500 j and the kinetic energy is 960 j.

the potential energy is 2,000 j and the kinetic energy is 480 j.

the potential energy is 2,000 j and the kinetic energy is 960 j.

Explanation:

Step1: Calculate potential energy

The formula for potential energy is \(PE = mgh\). The height \(h\) after falling \(4.9m\) is \(20 - 4.9=15.1m\). Given \(m = 10kg\), \(g = 9.8m/s^{2}\), then \(PE=10\times9.8\times15.1 = 1479.8\approx1500J\)

Step2: Calculate kinetic energy

The formula for kinetic energy is \(KE=\frac{1}{2}mv^{2}\). We first find the velocity \(v\) using the equation \(v = v_{0}+at\). Since \(v_{0} = 0\), \(a=- 9.8m/s^{2}\), \(t = 1s\), then \(v=0+( - 9.8)\times1=- 9.8m/s\) (speed is \(|v| = 9.8m/s\)). Substitute \(m = 10kg\) and \(v = 9.8m/s\) into the kinetic - energy formula: \(KE=\frac{1}{2}\times10\times(9.8)^{2}=480.2\approx480J\)

Answer:

The potential energy is \(1500J\) and the kinetic energy is \(480J\).