# Air resistance (pebble throwing)

• jojoking
In summary, the conversation discusses a question about a pebble thrown upwards without air resistance and provides a solution for finding the height the pebble reaches. The conversation then shifts to finding the height with air resistance and discusses the equation and integration needed for solving it. The expert also reviews the steps taken and provides pointers for solving the problem.

#### jojoking

i have solved the question of a pebble thrown upwards without air resistance
speed 10m/s mass 0.02kg ma=w, w=-mg

man on cliff 50 feet high throws pebble upwards so it finishes in sea,
what height does it reach v=0 t = 10/g approx =1
since motion started at t =0 & duration of time 1s
x = 100/g - 100/2g is approx 5.1m so maximum height 55.1 m

BUT
i now need to find height with air resistance 0.008 v
any pointers to x value warmly recieved
cheersjk

Again, mass times acceleration equals force.

Without air resistance, the only force its weight: -mg so you have
$$m\frac{dv}{dt}= -mg$$
The easy solution to that is v= -gt+ C. Since the initial velocity is 10 m/s
v(t)= dx/dt= -gt+ 10. Integrate again to get x as a function of t. Solve v(t)= -gt+ 10 to find when it stops going up, put that value of t into the x fuction to find the highest point.

I said that to review what you must have done. Now, with air resistance, the force is -mg- 0.008v (negative because friction force always opposes v).

$$m\frac{dv}{dt}= -mg- 0.008v$$
You can rewrite that as
[tex]\frac{mdv}{mg+0.008v}= -dt[/itex]
and integrate both sides to find v as a function of t. From there the rest of the problem is the same.

i understand your reasoning, thank you

cheers jk

## 1. What is air resistance in the context of throwing a pebble?

Air resistance is the force that acts against the motion of an object through the air. In the context of throwing a pebble, it is the resistance that the air exerts on the pebble as it travels through the air.

## 2. How does air resistance affect the trajectory of a thrown pebble?

Air resistance can cause a pebble to deviate from its intended trajectory, as it slows down the pebble's speed and alters its direction. This is because the force of air resistance is greater in the direction opposite to the motion of the pebble, thus causing it to slow down and change direction.

## 3. Is air resistance the same for all objects?

No, air resistance can vary for different objects depending on their shape, size, and speed. Objects with larger surface areas or traveling at higher speeds experience greater air resistance, while objects with smaller surface areas or slower speeds experience less air resistance.

## 4. How can air resistance be reduced when throwing a pebble?

Air resistance can be reduced by throwing the pebble with a streamlined shape, such as a smooth and rounded rock, as it will encounter less air resistance. Additionally, throwing the pebble with greater force can also help to overcome air resistance.

## 5. Can air resistance be completely eliminated?

No, air resistance cannot be completely eliminated as it is a natural force that exists in our atmosphere. However, it can be minimized through techniques like throwing with a streamlined shape and greater force, as well as by accounting for air resistance in calculations and making adjustments to the trajectory of the throw.