You decide to drop a melon from rest from the first observation platform of the

Question

You decide to drop a melon from rest from the first observation platform of the Eiffel Tower. The initial height h from which the melon is released is 58.3 m above the head of your French friend Pierre, who is standing on the ground right below you. At the same instant you release the melon, Pierre shoots an arrow straight up with an initial velocity of 251.m/s. (a) At what height above Pierre’s head do the melon and the arrow collide? (b) What are the velocities of the melon and the arrow at the moment of collision?

Explanation / Answer

use the kinematics equation for each thing: .     final position  = initialposition + initial velocity * time   + (1/2) a t2 .   melon:           y final = 58.3   +    0    -   (1/2) * 9.8 * t2 .   arrow:           y final =   0   +     251 t    - (1/2) *9.8 * t2 . Set them equal to each other: .                 251 t   - 4.9 t2   =   58.3    -   4.9t2 . Solve for t, the time that theycollide:            251 t   =  58.3          t = 0.23227 . Then plug back in to get yfinal:        y = 58.3 - 4.9 * 0.232272  =    58.04 meters . To get their velocities... .       final velocity = initial velocity - gt . melon:         finalvelocity = - 9.80 * 0.23227   =    - 2.276m/s     (note: moving downward, sonegative) . arrow:         finalvelocity =   251 - 9.80 * 0.23227 =   248.7 m/s . Solve for t, the time that theycollide:            251 t   =  58.3          t = 0.23227 . Then plug back in to get yfinal:        y = 58.3 - 4.9 * 0.232272  =    58.04 meters . To get their velocities... .       final velocity = initial velocity - gt . melon:         finalvelocity = - 9.80 * 0.23227   =    - 2.276m/s     (note: moving downward, sonegative) . arrow:         finalvelocity =   251 - 9.80 * 0.23227 =   248.7 m/s

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