Q.4.

Expert-verified
Found in: Page 104

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

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

# A projectile is launched at an angle of .a. Is there any point on the trajectory where and are parallel to each other? If so, where?b. Is there any point where and are perpendicular to eachother? It so, where?

a. and do not become parallel to each other at any point on the trajectory.

b. and become perpendicular to each other at the highest point on the trajectory.

See the step by step solution

## Step.1

The initial velocity of the object is . Since, it is given that the projectile is launched at an angle is in a direction that makes an angle with the -axis. Let's resolve in to and components; and .

The only force acting on the object is the weight. Hence the acceleration of the object is equal to the gravitational acceleration , which always acts downward (in negative -direction).

## Step 2

Consider the horizontal motion. Since there is no acceleration in the -direction, remains unchanged during the projectile.

Now consider the vertical motion. Due to the gravitational acceleration in the negative direction , reduces and becomes zero. Now since there is no vertical velocity the object can't go higher than this point; this is the maximum height of the projectile.

After that the vertical motion of the object is like a free fall.

## Step.3

Let's say the maximum height it reaches is and the final displacement is . The path of the projectile can be sketched as given below.

## (a)

From the diagram above we can see that, and do not become parallel to each other at any point on the trajectory.

## (b)

From the diagram above we can see that, and become perpendicular to each other at the highest point on the trajectory.