469.24m. An airplane flying 60m/s at a height of 300m dropped a sack of flour that stack the ground 469.24m from the point of release.
This is a example of horizontal parabolic projectile motion,and we represents this motion in the coordinate axis, which means that the velocity has components in x axis and y axis.
The equation of components on the x axis.
[tex]v_{0}x=\frac{x}{t}[/tex], where x is the distance and Vox the initial velocity before the drop
The equation of components on the y axis.
[tex]y = v_{0}yt+\frac{gt^{2} }{2}[/tex], where y is the height, and the velocity in y component before the drop is 0, reducing the equation to [tex]y = \frac{gt^{2} }{2}[/tex]
Clear t from both the equation of components on the x axis and the y axis:
[tex]t=\frac{x}{v_{0} x}[/tex] and [tex]t=\sqrt{\frac{2h}{g}}[/tex]
Equating both equations and clearing the distance x:
[tex]\frac{x}{v_{0} x}=\sqrt{\frac{2h}{g}}\\x={v_{0} x}\sqrt{\frac{2h}{g}}[/tex]
Substituting the values:
[tex]x=60\frac{m}{s} \sqrt{\frac{2(300m)}{9.81\frac{m}{s^{2} } }}=469.24m[/tex]
