Question

question 10 of 20
an arrow has a mass of 0.08 kg and is flying 1.2 m above the ground with a speed of 32 m/s. what is the total mechanical energy of the arrow? the acceleration due to gravity is 9.8 m/s².
a. 4 j
b. 42 j
c. 1 j
d. 40 j

Explanation:

Step1: Calculate kinetic energy

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$. Given $m = 0.08\ kg$ and $v = 32\ m/s$, we have $K=\frac{1}{2}\times0.08\times32^{2}=\frac{1}{2}\times0.08\times1024 = 40.96\ J$.

Step2: Calculate potential energy

The formula for gravitational - potential energy is $U = mgh$. Given $m = 0.08\ kg$, $g = 9.8\ m/s^{2}$, and $h = 1.2\ m$, we have $U=0.08\times9.8\times1.2 = 0.9408\ J$.

Step3: Calculate total mechanical energy

The total mechanical energy $E = K + U$. So $E=40.96+0.9408 = 41.9008\approx42\ J$.

Answer:

B. 42 J