A ball is thrown straight up from the surface of the Earth with the same initial…

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Kinematics · Kinematics

Problem

A ball is thrown straight up from the surface of the Earth with the same initial speed on two different celestial bodies. On Earth the acceleration due to gravity is gE=9.8 m/s2g_{E}=9.8\,\text{m/s}^2, while on the Moon it is gM=1.6 m/s2g_{M}=1.6\,\text{m/s}^2. If tEt_{E} is the total time of flight on Earth and tMt_{M} is that on the Moon, which relation is correct? (a) tM=gEgM tE   (≈2.5 tE)t_{M}=\sqrt{\dfrac{g_{E}}{g_{M}}}\,t_{E}\;\,(\approx 2.5\,t_{E}) (b) tM=gEgM tE   (≈6.1 tE)t_{M}=\dfrac{g_{E}}{g_{M}}\,t_{E}\;\,(\approx 6.1\,t_{E}) (c) tM=gE−gMgM tE   (≈5.1 tE)t_{M}=\dfrac{g_{E}-g_{M}}{g_{M}}\,t_{E}\;\,(\approx 5.1\,t_{E}) (d) tM=gMgE tE   (≈0.16 tE)t_{M}=\dfrac{g_{M}}{g_{E}}\,t_{E}\;\,(\approx 0.16\,t_{E})

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