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Q.31

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

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 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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