posted by Blair on .
When the dried up seed pod of a scotch broom plant bursts open, it shoots out a seed with an initial velocity of 2.2 m/s at an angle of 60.0° above the horizontal.
If the seed pod is 0.8 m above the ground, how long does it take for the seed to land? (Neglect air resistance.)
What horizontal distance does it cover during its flight?
Vo = 2.2m/s @ 60 deg.
Vo(v) = 2.2sin60 = 1.91m/s.
Vf^2 = Vo^2 + 2gd,
d = (Vf^2-Vo^2) / 2a,
d = (0-(1.91)^2 / -19.6 = 0.186m,up.
Vf = Vo + gt,
t = (Vf - Vo) / a,
t = (0 - 1.91 / -9.8 = 0.195s,up.
d = 0.8 + 0.186 = 0.986m above ground.
d = Vo + 0.5gt^2 = 0.986m,
0 + 0.5*9.8t^2 = 0.986,
4.9t^2 = 0.986,
t^2 = 0.20,
t = 0.447s, down.
T = t(up) + t(down) = 0.195 + 0.447 =
0.64s to land.
Vo(h) = 2.2cos60 = 1.1m/s.
d(h) = 1.1m/s * 0.64s. = 0.704m = hor