Question

At a construction site a pipe wrench struck the ground with a speed of 27 m/s. (a) From what height was it inadvertently dropped? (b) How long was it falling?

Answer 1

At a construction site a pipe wrench struck the ground with a speed of 27 m/s. (a) From what height was it inadvertently dropped?

**Solution.**

From the energy conservation law we have that at the ground level all potential energy is transformed to kinetic energy:

$$\begin{array}{l} m v^{2} / 2 = m g h, \\ h = \frac{v^{2}}{2 g} = (27 \, m / s)^{2} / (2 * 9.8 \, m / s^{2}) = 37.19 \, m \end{array}$$

**Answer.**

$$h = 37.2 \, m$$

(b) How long was it falling?

**Solution.**

We right the second Newton's law:

$$m \, d^{2} / dt^{2} \, x = -mg,$$

solving it we obtain

$$x = -g t^{2} / 2 + v_{0} t + x_{0}.$$

Initial coordinate is

$$x_{0} = h,$$

and initial speed is zero

$$v_{0} = 0.$$

At the ground level $x = 0$

$$\begin{array}{l} 0 = -g t^{2} / 2 + h \\ t = \sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 * 37.2 \, m}{9.8 \, m / s^{2}}} = 2.76 \, s \end{array}$$

**Answer.**

$$t = 2.8 \, s$$

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