6.02 × 10^4 ÷ 5.1 × 10^6
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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.
, where x is the distance and Vox the initial velocity before the drop
The equation of components on the y axis.
, where y is the height, and the velocity in y component before the drop is 0, reducing the equation to
Clear t from both the equation of components on the x axis and the y axis:
and
Equating both equations and clearing the distance x:
Substituting the values:
Answer:
Resultant displacement = 38.58 miles at an angle of 23.57° north of west.
Explanation:
Let north represent positive y direction and east represent positive x direction. Unit vector along x direction is represented by i and vector along unit vector along y direction is represented by j
Initial displacement = 17 miles north = 17 j miles
Final displacement = 24 miles at an angle of 40° west of north = 24 miles at an angle of 130° to positive x -axis
= (24 cos 130 i + 24 sin 130 j )
= (-15.43 i + 18.36 j ) miles
Total displacement = 17 j + (-15.43 i + 18.36 j) = -15.43 i + 35.36 j
Magnitude of displacement
Angle to positive x -axis = tan⁻¹(35.36/-15.43) = 113.57°
Resultant displacement = 38.58 miles at an angle of 23.57° west of north.