Question

A rock is thrown upward from the level ground in such a way that the maximum height of its flight is equal to its horizontal range R.
(a) At what angle θ is the rock thrown? °
(b) In terms of its original range R, what is the range Rmax the rock can attain if it is launched at the same speed but at the optimal angle for maximum range? Rmax =
(c) Would your answer to part (a) be different if the rock is thrown with the same speed on a different planet? Yes No

Answer 1

Answer

a) For the rock

$\dfrac{v_t^2sin 2\theta}{g} = \dfrac{v_t^2sin^2\theta}{2g}$

$2sin\thetacos\theta = \dfrac{sin^2\theta}{2}$

$2cos\theta = \dfrac{sin\theta}{2}$

$tan\theta = 4$

$\theta = tan^{-1} 4$

$\theta = 76^0$

b) $\theta = 45^0$ for maximum range

$\dfrac{d_{max}}{d}=\dfrac{(v_tcos 45^0)(2v_tsin 45^0)g}{(v_tcos 76^0)(2v_tsin 76^0)g}$

$\dfrac{d_{max}}{d}=\dfrac{0.707\times 0.707)}{0.97\times 0.242}$

$\dfrac{d_{max}}{d}=2.129$

$d_{max}=2.129 d$

c) The value of θ is the same on every planet as g divides out.