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Q.31

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Found in: Page 200

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# Derive Equations 8.3 for the acceleration of a projectile subject to drag.

Newton's second law of motion along direction .

Newton's second law of motion along direction .

See the step by step solution

## Step 1: Given Information

Consider a ball of mass in a projectile motion with initial velocity. Let the trajectory of the ball makes an angle with the axis.

## Step 2: Velocity of x and y component

Let's consider the -component of the velocity as follow:

Then, the-component of the velocity is same as above, and it is

## Step 3: x component of the drag force

The magnitude of the drag force is given by

where indicates the density of the air, remains the speed of the ball, shows the drag coefficient and means the projected area of the ball.

The component of the drag force is given by

## Step 4: Y component of the drag force

To find the final expression, we are using the given equation.

Similarly the component of the drag force is given as follow

## Step 5: Applying the Newton's second law

Let's apply the Newton 's second law of motion along the direction,

## Step 6: Applying the Newton's second law along with y direction

As same as the step 5, we are applying Newton's second law of motion along direction,

## Step 7: Final Answer

Newton's second law of motion along direction .

Newton' s second law of motion along direction,

.

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