The information given is
- The initial velocity is Vo=28.0m/s
- The launch angle is θ=350
- Gravity acceleration is ay=−9.81m/s2
- The starting position for the move is xo=0mandyo=0m
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Components of the initial velocity.
Horizontal component.
cos(350)=VoVoxcos(350)Vo=V0xV0x=Vocos(350)Vox=28.0m/s×cos(350)Vox=22.9m/s
Vertical component.
sin(350)=VoVoysin(350)Vo=V0yV0y=Vosin(350)Voy=28.0m/s×sin(350)Voy=16.1m/s
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The maximum height is calculated with the following equation.
ΔYmax=2ayVfy2−Voy2
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Where.
Voy is the initial vertical velocity.
Vfy is the velocity at the maximum height.
ay is the acceleration of gravity.
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Remember that at the top, the vertical component of velocity is zero.
Vfy=0m/s
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Evaluating numerically.
ΔYmax=2ayVfy2−Voy2ΔYmax=2×−9.81m/s2(0m/s)2−(16.1m/s)2ΔYmax=13.2m
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!!Answer.
The maximum height is ΔYmax=13.2m
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Flight time is calculated using the following equation.
Vfy=Voy+ayt
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where
Voy is the initial vertical velocity.
Vfy is the final vertical velocity.
ay is the vertical acceleration.
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Remember that if the movement is symmetrical, the vertical velocity with which it reaches the ground is of the same magnitude but in the opposite direction
Vfy=−Voy .
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Obtaining the expression for time.
Vfy=Voy+aytVoy+ayt=Vfyayt=Vfy−Voyt=ayVfy−VoyifVfy=−Voyt=ay−Voy−Voyt=ay−2Voy
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Evaluating numerically.
t=ay−2Voyt=−9.81m/s2−2×16.1m/st=3.28s
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!!Answer.
Flight time is t=3.28s
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The distance traveled is given by the following equation.
X=X0+Voxt
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where.
Vox is the horizontal velocity.
t Is time.
Xo is the starting position.
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Evaluating numerically
X=X0+VoxtX=0m+22.9m/s×3.28sx=75.1m
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!!Answer
The maximum horizontal reach is x=75.1m
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