Range, Height and TimeProjectile PathParameterized CurveHeightRangeTimeDifferent HeightsRange, Height and TimeRange, Height and TimeProjectile PathProjectile PathAll projectiles follow the All projectiles follow the same shape path.same shape path.This path is a parabola.This path is a parabola.Acceleration is constant.Acceleration is constant.Horizontal velocity is also Horizontal velocity is also constant.constant.Velocity and position Velocity and position change.change.Parameterized CurveParameterized CurveThe two equations of motion can be combined to give The two equations of motion can be combined to give an equation for the trajectory.an equation for the trajectory.We’ve set the origin to We’ve set the origin to xx00 = 0, = 0, yy00 = 0. = 0.)/()/(/00202100221000xyxyxxvxvvxgyytvgtyvxtxtvxHeightHeightThe maximum height occurs when The maximum height occurs when vvyy = 0. = 0.This is identical to 1-dimensional motion.This is identical to 1-dimensional motion.From the height can the initial velocity be estimated?From the height can the initial velocity be estimated?gvgvvgvgytvgtygvtvgtvyyyyyyyy2/)()/()/(/20002021022100RangeRangeThe The rangerange of a projectile is of a projectile is the horizontal distance.the horizontal distance.The simplest range to find is The simplest range to find is for a projectile returning to its for a projectile returning to its initial height.initial height.This is linked to the angle of This is linked to the angle of the initial velocity.the initial velocity.gvxgvxgvvxtvxgvttvgtyxxyy/2sin/sincos2)/2(/20202000000221Time Time The time in flight can be The time in flight can be determined by height alone.determined by height alone.The “hang time” is just this The “hang time” is just this time in flight.time in flight.A 1 m jump will be in the air A 1 m jump will be in the air for about 0.9 s.for about 0.9 s.The range doesn’t matter.The range doesn’t matter.ghtghttgtgthgtvvgtvtopyyy/22/2)(22100Different HeightsDifferent HeightsNot all motion starts and stops at the same height.Not all motion starts and stops at the same height.The difference in height can be found by the full set of The difference in height can be found by the full set of equations.equations.Let Let yy be some non-zero value. be some non-zero
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