Some people in a hotel are dropping water balloons from their open window on to the ground below. The balloons take 0.15 s to pass your 1.6-m-tall window. Where should security look for the raucous hotel guests?

Answer :

Explanation:

Let us assume that the initial velocity is u. And, according to the kinematics,

                s = [tex]ut + \frac{1}{2}gt^{2}[/tex]

           ut = s - [tex]\frac{1}{2}gt^{2}[/tex]

Putting the given values into the above formula as follows.

            ut = s - [tex]\frac{1}{2}gt^{2}[/tex]

    [tex]u \times 0.15 s = 1.6 - \frac{1}{2}9.8 \times (0.15 s)^{2}[/tex]

            u = 9.93 m/s

Hence, the required height will be calculated as follows.

               h = [tex]\frac{u^{2}}{2g}[/tex]

                  = [tex]\frac{(9.93)^{2}}{2 \times 9.8}[/tex]

                  = 5.03 m

Thus, we can conclude that security look for the raucous hotel guests at 5.03 m.

Answer:

Security should look for the raucous hotel guests at height of  [tex]5.03[/tex] meters

Explanation:

Given

Height of the window [tex]= 1.6[/tex] meters

Time taken by balloon to pass the window [tex]= 0.15[/tex] seconds

As per second law of motion for objects moving upward

[tex]h = u*t - \frac{1}{2} gt^2\\[/tex]

Substituting the given values we get -

[tex]1.6 = u * 0.15 - 0.5 * 9.8 * 0.15^2[/tex]

u = [tex]\frac{1.6 + 0.5 * 9.8 * 0.15^2}{0.15}[/tex]

[tex]u = 9.93 \frac{m}{s}[/tex]

Security should look for the raucous hotel guests at height [tex]"h"[/tex]

Here

[tex]h = \frac{v^2}{2* g}[/tex]

Substituting the values in above equation, we get -

[tex]h = \frac{9.93^2}{2 * 9.81} \\h = 5.03[/tex]

Security should look for the raucous hotel guests at height of  [tex]5.03[/tex] meters