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A cannon battery simultaneously fires two shells in the parabolic trajectories as shown. Which shell hits the ground first?
A cannon battery simultaneously fires two shells in the parabolic trajectories as shown. Which shell hits the ground first?
A) A
A) A
B) B
B) B
C) both at the same time
C) both at the same time
D) need more information
D) need more information
Solution: B. The time the shell spends in the air is uniquely determined its motion in the vertical direction. Because shell A reaches a higher altitude, it must spend more time in the air. The following equation solved for time interval during the second half of the motion demonstrates this:
Solution: B. The time the shell spends in the air is uniquely determined its motion in the vertical direction. Because shell A reaches a higher altitude, it must spend more time in the air. The following equation solved for time interval during the second half of the motion demonstrates this:
Δy = viyΔt + ½ayΔt2
Δy = viyΔt + ½ayΔt2
Δy = 0 + ½ayΔt2
Δy = 0 + ½ayΔt2
Δt = √ (2Δy/ay)
Δt = √ (2Δy/ay)
Since the accelerations are the same, the time for the larger vertical distance is larger. A similar analysis can be done for the first half of the motion.
Since the accelerations are the same, the time for the larger vertical distance is larger. A similar analysis can be done for the first half of the motion.
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