Question

a ball with a mass of 1.0 kg is 11 m high and falling at a speed of 5.0 m/s. which equation shows the total initial energy? (1 point)

total energy = -\frac{1}{2}(1.0)(5.0)^{2}-(1.0)(11)

total energy = \frac{1}{2}(1.0)(5.0)^{2}-(1.0)(9.8)(11)

total energy = -\frac{1}{2}(1.0)(5.0)^{2}+(1.0)(9.8)(11)

total energy = \frac{1}{2}(1.0)(5.0)^{2}+(1.0)(9.8)(11)

Explanation:

Step1: Calculate kinetic energy

The formula for kinetic energy \(K = \frac{1}{2}mv^{2}\). Here, \(m = 1.0\space kg\) and \(v=5.0\space m/s\). Kinetic energy is positive as it is a measure of motion, so \(K=\frac{1}{2}(1.0)(5.0)^{2}\).

Step2: Calculate potential energy

The formula for gravitational potential energy \(U = mgh\). Here, \(m = 1.0\space kg\), \(g = 9.8\space m/s^{2}\), and \(h = 11\space m\). Potential energy is positive as it is stored energy, so \(U=(1.0)(9.8)(11)\).

Step3: Calculate total initial energy

The total initial energy \(E=K + U\). Substituting the values of \(K\) and \(U\) from above, we get \(E=\frac{1}{2}(1.0)(5.0)^{2}+(1.0)(9.8)(11)\).

Answer:

Total energy \(=\frac{1}{2}(1.0)(5.0)^{2}+(1.0)(9.8)(11)\) (the fourth option)