Projectile Motion
Problem:
Suppose that an airplane flying at 60 m/s, at a height of 300m drops a sack of flour.
How far from the point of release would the sack have traveled when it struck the ground?
How far from the point of release would the sack have traveled when it struck the ground?
Graphs* and explanations:
*click on graph to enlarge it
xt graph:
This graph represents the horizontal motion of the flour. It also indicates that the flour has a constant velocity from the beginning of its fall, untill the flour hit the ground.
Vxt Graph:
This represents the constant velocity of the flour because the line is horizontal, which means that the movement is contant: therfore a constant velocity.
yt graph:
This represents the vertical motion of the flour. This shows the movement as the sack of flour first begins to fall and continues downwards.
Vyt graph:
This graph shows the velocity of the flour in the vertical motion. The velocity is negative, and decreases consistently.
Equations:
Y = 1/2 * gt^2 + V0y + Y0
-300m = 1/2 * (-9.8 m/s^2*t^2) + 0
t = 7.8 s
X = VxT + X0
ΔX = 60 m/s * 7.8 s
ΔX = 486 m. (this is the distance that the sack traveled once it hit the ground.)
-300m = 1/2 * (-9.8 m/s^2*t^2) + 0
t = 7.8 s
X = VxT + X0
ΔX = 60 m/s * 7.8 s
ΔX = 486 m. (this is the distance that the sack traveled once it hit the ground.)
Equation explanations:
ΔX: the displacement of the x-axis (horizontal) shows how far the sack travelled once it hit the ground.
VxT: shows the velocity of the sack of flour.
t: represents the time it tool for the flour to hit the ground.
ΔY: shows the distance that the sack travelled vertically.
g: the rate at which the sack accelerated downwards.
t: the time that it took for the flour to hit the ground.
V0Y: the standard vertical measurement (y).
VxT: shows the velocity of the sack of flour.
t: represents the time it tool for the flour to hit the ground.
ΔY: shows the distance that the sack travelled vertically.
g: the rate at which the sack accelerated downwards.
t: the time that it took for the flour to hit the ground.
V0Y: the standard vertical measurement (y).