Answer
a) For the rock
[tex]\dfrac{v_t^2sin 2\theta}{g} = \dfrac{v_t^2sin^2\theta}{2g}[/tex]
[tex]2sin\thetacos\theta = \dfrac{sin^2\theta}{2}[/tex]
[tex]2cos\theta = \dfrac{sin\theta}{2}[/tex]
[tex]tan\theta = 4[/tex]
[tex]\theta = tan^{-1} 4[/tex]
[tex]\theta = 76^0[/tex]
b) [tex]\theta = 45^0[/tex] for maximum range
[tex]\dfrac{d_{max}}{d}=\dfrac{(v_tcos 45^0)(2v_tsin 45^0)g}{(v_tcos 76^0)(2v_tsin 76^0)g}[/tex]
[tex]\dfrac{d_{max}}{d}=\dfrac{0.707\times 0.707)}{0.97\times 0.242}[/tex]
[tex]\dfrac{d_{max}}{d}=2.129[/tex]
[tex]d_{max}=2.129 d[/tex]
c) The value of θ is the same on every planet as g divides out.
