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Transcript of Projectile Motion
AT AN ANGLE
FREE-FALL HORIZONTAL x=V t x y= at 1
2 _ 2 A projectile is launched with an initial horizontal velocity from an elevated position and follows a parabolic path to the ground. Predictable unknowns include the initial speed of the projectile, the initial height of the projectile, the time of flight, and the horizontal distance of the projectile. A soccer ball is kicked
horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball. 1
2 _ 2 t=4.4 sec 35.0 m=V (4.4 s) x V =7.95 m/s x -22.0 m= (-10)t AT AN ANGLE A projectile is launched at an angle to the horizontal and rises upwards to a peak while moving horizontally. Upon reaching the peak, the projectile falls with a motion that is symmetrical to its path upwards to the peak. Predictable unknowns include the time of flight, the horizontal range, and the height of the projectile when it is at its peak. V =V sin( )
V =V cos( )
t = ix iy i i up V iy __ g t =2(t )
y=V (t )+ a(t )
x=V (t ) total up iy up 1
2 up 2 ix total A football is kicked with an initial
velocity of 25 m/s at an angle of 45-degrees
with the horizontal. Determine the time of flight,
the horizontal distance, and the peak height of the football. V =25 sin(45)
V =17.678 m/s iy iy V =25cos(45)
V =17.678 m/s ix ix t =
t =1.7678 sec
t =3.5356 sec y=17.678(1.7678)+ 10(1.7678) y=46.877 m total up up 17.678
10 ______ 1
2 __ 2 x=17.678 (3.3536)
x=59.285 m FREE-FALL A free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall."