A worker's hammer is accidentally dropped from the 20th floor of a building under construction. With what velocity does it strike the pavement 304 ft below, and what time t is required?

Question

Engineering

Marisol Vazquez

15 October, 15:32

A worker's hammer is accidentally dropped from the 20th floor of a building under construction. With what velocity does it strike the pavement 304 ft below, and what time t is required?

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Answers (1)

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Gabriella Page · Answer 1

Final Velocity (Vf) = 139.864 ft/s

Time (t) = 4,34 s

Explanation:

This is a free fall problem, to solve it we will apply free fall concepts:

In a free fall the acceletarion is gravity (g) = 9,81 m/s2, if we convert it to ft/s^2 = g = 32.174 ft/s^2

Final velocity is Vf = Vo + g*t[tex]Vf^{2} = Vo^{2} + 2*g*h

where h is height (304 ft in this case).

Vo = 0 since the hammer wasn't moving when it stared to fall

Then Vf^2 = 0 + 2 * 32.174 ft/s^2 * 304 ft

Vf^2 = 19,561.8224 ft^2/s^2

Vf=[sqrt{19561.8224 ft^2/s^2}

Vf=139.864 ft/s

Time t = (Vf-Vo) / g = > (139.864 ft/s-0) / 32.174 ft/s^2 = 4.34 sec

Good luck!