Question

Assume the sand bags are rectangular in shape and have a mass of 0.3kg and a length of 25 cm and a width of 11 cm. The terminal velocity is 14.77m/s if the drag coefficient is 0.8 and the density of the air is 1.225kg/m3. a) How long would it take for this object to reach its terminal velocity if we ignore drag until the sandbag reaches its terminal velocity? b) The sandbag reaches its terminal velocity just before it hits the ground. How tall is the tower?

Answer 1

a) 1.51 seconds

b) 11.17 meters

Explanation:

Given:

Mass (m) = 0.3 kg

Length (l) = 25 cm = 0.25 m

Width (w) = 11 cm = 0.11 m

Terminal velocity (vt) = 14.77 m/s

Density of the air (d) = 1.225 kg/m³

Drag coefficient = 0.8

a)

We can determine the time using the following formula since we know the terminal velocity:

`\begin{gathered} v_t=u+gt \\ \\ \text{ in this case the initial velocity is 0, therefore:} \\ \\ 14.77=0+9.8t \\ \\ t=(14.77)/(9.8) \\ \\ t=1.51\text{ sec} \end{gathered}`

b)

Now, knowing the time, determine the height:

`\begin{gathered} h=(1)/(2)gt^2 \\ \\ \text{ We replacing:} \\ \\ h=(1)/(2)(9.8)(1.51)^2 \\ \\ h=11.17\text{ m} \end{gathered}`