Q46P - Fundamentals Of Physics

Question

Raindrops fall 1700 m from a cloud to the ground. (a) If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? (b) Would it be safe to walk outside during a rainstorm?

Step-by-Step Solution

Answer

1. The velocity of the raindrop is 183 m/s .
2. It would not be safe to walk outside during the rainstorm.

Step 1: Given information

• $\mathrm{Initial} \mathrm{Velocity} \left({\mathrm{v}}_{\mathrm{i}}\right)=0 \mathrm{m}/\mathrm{s}$.
• $\mathrm{Displacement} \left(\mathrm{y}\right)=1700 \mathrm{m} .$
• $\mathrm{Acceleration} \left(\mathrm{a}\right)=\mathrm{Gravitational} \mathrm{Acceleration}=9.8 \mathrm{m}/{\mathrm{s}}^2.$

Step 2: Understanding the concept

The problem deals with the kinematic equation of motion in which the motion of an object is described at constant acceleration. As the air resistance was neglected in this problem, the acceleration will be constant in the given situation. The raindrops would be acted upon by only gravitational acceleration. 

Using the kinematic equation, the velocity of the drop can be found. 

 

The final velocity in the kinematic equation is given by,

 ${{\mathrm{v}}_{\mathrm{f}}}^2={{\mathrm{v}}_0}^2+2\mathrm{ay} \left(\mathrm{i}\right)$                                                                                                             

Here ${\mathrm{v}}_0$ is the initial velocity, a is acceleration as y is the displacement.

Step 3: (a) Calculating the velocity of raindrops

As there is no air resistance present, acceleration will be constant throughout the problem. Assuming the downward direction is positive and the upward is negative.

Using notation given in equation (i) the velocity can be written as 

${\mathrm{v}}^2={{\mathrm{v}}_0}^2+2\mathrm{ay}$

Substitute the given values in the above equation.

$$\begin{gathered} {\mathrm{v}}^2=0+\left(2\times 9.8 \mathrm{m}/{\mathrm{s}}^2\times 1700 \mathrm{m}\right) \\ {\mathrm{v}}^2=33320 {\mathrm{m}}^2/{\mathrm{s}}^2 \\ \mathrm{v}=182.53 \\ \approx 183 \mathrm{m}/\mathrm{s} \end{gathered}$$

Thus, the velocity of the drop is $183 \mathrm{m}/\mathrm{s}$ .

Step 4: (b) Finding out whether it is safe to walk outside during the rainstorm.

From part (a) we can see that the speed of raindrops is quite high. The mass of the raindrop is very small. But in a rainstorm, there will be several raindrops hitting the person at the same time. Even a small mass hitting a person with such a high velocity will be extremely dangerous. Therefore, it is unsafe to walk outside during a rainstorm.