Answer
19 meters
Work Step by Step
We know the following equation:
$R=\frac{v_0^2sin(2\theta)}{g}$
We find the initial velocity:
$v_0=\sqrt{\frac{Rg}{sin(2\theta)}}$
$v_0=\sqrt{\frac{(28)(9.81)}{sin(2(40^{\circ}))}}=16.7\ m/s$
We know the following equations:
$\Delta x = v_{0x}t = 16.7cos(40)t$
$\Delta y = v_{0y}t-\frac{1}{2}gt^2=16.7sin(40)t-4.9t^2$
We know:
$tan\theta = \frac{opposite}{adjacent}$
Thus, we find:
$tan15=\frac{12.79t}{10.73t-4.9t^2}$
$t=1.485 \ s$
We multiply this by the equation for x to find:
$x = 16.7cos(40)t=16.7cos(40)(1.485)=19 \ meters$
