Question

3. Suppose that an airplane flying 60 m/s, at a height of 300m, dropped a sack of flour (pere the effect

Answer 1

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.

$v_{0}x=\frac{x}{t}$, where x is the distance and Vox the initial velocity before the drop

The equation of components on the y axis.

$y = v_{0}yt+\frac{gt^{2} }{2}$, where y is the height, and the velocity in y component before the drop is 0, reducing the equation to $y = \frac{gt^{2} }{2}$

Clear t from both the equation of components on the x axis and the y axis:

$t=\frac{x}{v_{0} x}$ and $t=\sqrt{\frac{2h}{g}}$

Equating both equations and clearing the distance x:

$\frac{x}{v_{0} x}=\sqrt{\frac{2h}{g}}\\x={v_{0} x}\sqrt{\frac{2h}{g}}$

Substituting the values:

$x=60\frac{m}{s} \sqrt{\frac{2(300m)}{9.81\frac{m}{s^{2} } }}=469.24m$