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a helicopter (m = 3250 kg) is cruising at a speed of 56.9 m/s at an altitude of 185 m. what is the total mechanical energy (ke + pe) of the helicopter?
1.12×10⁷ j
3.91×10⁷ j
5.26×10⁷ j
2.27×10⁸ j
6.91×10⁷ j

Explanation:

Step1: Calculate kinetic energy ($KE$)

The formula for kinetic energy is $KE=\frac{1}{2}mv^{2}$. Given $m = 3250\ kg$ and $v=56.9\ m/s$.
$KE=\frac{1}{2}\times3250\times(56.9)^{2}=\frac{1}{2}\times3250\times3237.61 = 1625\times3237.61=5.26\times10^{6}\ J$

Step2: Calculate potential energy ($PE$)

The formula for gravitational potential energy is $PE = mgh$. Given $m = 3250\ kg$, $g = 9.8\ m/s^{2}$, and $h = 185\ m$.
$PE=3250\times9.8\times185=3250\times1813=5.89\times10^{6}\ J$

Step3: Calculate total mechanical energy ($E$)

$E=KE + PE$.
$E=(5.26\times 10^{6})+(5.89\times 10^{6})=1.115\times10^{7}\approx1.12\times10^{7}\ J$

Answer:

$1.12\times 10^{7}\ J$