Answer
Jesse Owens' record in Melbourne would have been longer by $~~1.0~cm$
Work Step by Step
We can write a general expression for the range:
$x = \frac{v_0^2~sin~2\theta}{g}$
We can write an expression for the range in Berlin:
$x_B = \frac{v_0^2~sin~2\theta}{g_B} = 8.09~m$
We can write an expression for the range in Melbourne:
$x_M = \frac{v_0^2~sin~2\theta}{g_M}$
We can find $x_M$:
$\frac{x_M}{x_B} = \frac{\frac{v_0^2~sin~2\theta}{g_M}}{\frac{v_0^2~sin~2\theta}{g_B}}$
$\frac{x_M}{x_B} = \frac{g_B}{g_M}$
$x_M = \frac{g_B}{g_M}~x_B$
$x_M = (\frac{9.8128~m/s^2}{9.7999~m/s^2})~(8.09~m)$
$x_M = 8.10~m$
Jesse Owens' record in Melbourne would have been longer by $~~1.0~cm$
