Q.31

Expert-verifiedFound in: Page 200

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 .

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

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

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

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

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

Similarly the component of the drag force is given as follow

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

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

Newton's second law of motion along direction .

Newton' s second law of motion along direction,

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