Question

At a construction site, a pipe wrench stuck the ground with a speed of 24 m/s(a)From what height was it inadvertently dropped? (b)How long was it falling? (c)Sketch graphs of y,v and a versus t for the wrench.

Short answer

(a) Height (H) from which the pipe wrench was dropped 29.4 m .

(b) Time (t) required for the pipe wrench to reach the ground 2.45 sec .

(c) The graph of y, v, and a versus t is plotted.

Step-by-step solution

Given data

The speed at which a pipe wrench stuck to the ground,$v=24\mathrm{m}/\mathrm{s}$ .

The initial velocity of a pipe wrench is$v_0=0\mathrm{m}/\mathrm{s}$.

The acceleration due to gravity is, $g=9.8\mathrm{m}/{\mathrm{s}}^2$.

Understanding the concept of free fall

The concept of free fall is used to solve this problem. The velocity when the pipe wrench is about to strike the ground. Assuming this as afree-fall motion, the acceleration of this wrench would be taken as gravitational acceleration.Using these given quantities in the kinematic equation to find the height.

The kinematic equations that can be used to solve this problem are,

$v^2=v_0^2+2as\left(s=H\right)$(i)

$v=v_0+at$(ii)

(a) Determination of Height (H) from which the pipe wrench was dropped

Assume the downward direction as positive and the upward direction as negative.

Substitute the value in equation (i)

$$\begin{gathered} {24}^2{m}^2/s^2=2\times 9.8m/s^s\times H \\ 576m^2/s^2=19.6m/s^2\times H \\ H=29.4\mathrm{m} \end{gathered}$$

So, the height from which the pipe wrench was dropped is$29.4\mathrm{m}$

(b) Time (t) required for the pipe wrench to reach the ground

Substitute the value in equation (ii)

$$\begin{gathered} 24m/s=0+9.8m/s^2·t \\ 24m/s=9.8m/s^2·t \\ t=2.4489 \\ \approx 2.45\mathrm{s} \end{gathered}$$

Therefore, the time taken for the pipe wrench to reach the ground is$2.45\mathrm{s}$.

(c) (i) Graph of displacement vs time and velocity vs time

(ii)Graph of velocity vs time

(iii)Graph of acceleration vs time