Three bears throw identical rocks but each bear throws their rock at different a

Question

Three bears throw identical rocks but each bear throws their rock at different angles. Which statement do you agree with if any, explain.

6. The following question appears on a physics exam: "Three bears are throwing identical rocks from a bridge to the river below. Papa Bear throws his rock upward at an angle of 30 degrees above the horizontal. Momma Bear throws hers perfectly horizontally. Baby Bear throws his at an angle of 30 degrees below the horizontal. Assuming that all three bears throw with the same speed, which rock will be traveling fastest when it hits the water?" Three students meet after the exam and argue about the correct answer. Student 1 says, "Baby Bear's rock will be going the fastest because it starts with a downward component of velocity." Student 2 says, "But Papa Bear's rock will stay in the air the longest, so it will have more time to speed up. I think his rock will be traveling the fastest. Student 3 says, "Papa Bear's rock does stay in the air longer, but part of that time it is moving upward and slowing down. I think Momma Bear's rock will be traveling fastest when it hits the water because it is in the air longer than Baby Bear's and it is speeding up all of the time." Which student (if any) do you agree with? Explain.

Explanation / Answer

All three students are wrong.
They are making an easy problem much too difficult by ignoring the power of the energy approach to problem solving.
Because each of the three rocks started with the same kinetic energy (same speed) and the same gravitational potential energy (same height), they must all end up with the same final kinetic energy before hitting the water.
All three rocks must therefore hit the water with the same speed.
Note that the three rocks will not hit the water at the same time, with the same direction of velocity, or at the same distance from the bridge. However, the energy method will not give us this information.

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