Final answer:
Ignoring air resistance, energy conservation allows us to calculate that a rock thrown off a bridge will have a final speed of 24.8 m/s based on its initial height and speed, independent of the direction due to the constant acceleration of gravity (g).
Step-by-step explanation:
A rock is thrown horizontally off a bridge, which is a classic problem in physics dealing with projectile motion and energy conservation. The student must understand how to analyze motion in both the horizontal and vertical components separately since they are independent of each other.
Projectile Motion and Energy:
Energy considerations show that the mechanical energy at the beginning is equal to the mechanical energy at the end if air resistance is negligible. The initial mechanical energy is the sum of the kinetic energy due to the initial speed and the potential energy due to the height of the bridge:
PE_initial + KE_initial = PE_final + KE_final
where PE is potential energy, KE is kinetic energy, and the '_initial' and '_final' subscripts denote the initial and final states, respectively. Given the information:
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- Initial height (h) = 20.0 m
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- Initial speed (v0) = 15.0 m/s
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- Gravitational acceleration (g) = 9.80 m/s2
The final speed (v) can then be found using the conservation of energy principle. For projectile motion, regardless of the direction thrown, as long as air resistance is neglected, the only acceleration acting on the projectile is due to gravity, which is g (9.80 m/s2).
Considering the above, if energy is conserved, the magnitude of the velocity will reach a calculated value based on the initial conditions provided. The result is independent of the direction thrown because neither the horizontal nor the vertical component of the initial velocity affects the total amount of mechanical energy at the start.