War time

Given, power is directly proportional to initial velocity,

If power is minimum, initial speed must be minimum.

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Construct a line from the tank to the target. Let the angle made by the line with ground be $\alpha$

$tan\alpha=\frac{86.6}{50} \implies \alpha=60°$

Let the angle between the line and projection be $\beta$ .

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This arrangement looks like projectile in an inclined plane .

Range in an inclined plane is given by-

$R=\dfrac{u^2 2cos\beta sin(\alpha+\beta)}{g cos^2\alpha}$

$u^2=\dfrac{R g cos^2\alpha}{2 cos\beta sin(\alpha+\beta)}$

Since R,g, $\alpha$ are constant. u to be minimum , $cos\beta sin(\alpha+\beta)$ must be maximum.

To find maximum value, differentiate it and equate it to 0.

We get $\alpha+\beta=45°+\frac{\alpha}{2}$

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According to diagram, $\alpha+\beta=\theta$ , $\alpha=60°$

Therefore, $\boxed{\theta=75°}$