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Q.38

Expert-verified
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

# A projectile with initial velocity experiences the variable force , where is in . a. What is the projectile’s speed at s?b. At what instant of time is the projectile moving parallel to theaxis?

a). The projectile's speed at is .

b). The projectile moving parallel to the axis at .

See the step by step solution

## Step 1: Given Information (Part a)

We are given the force in two dimensions in the form

.

is the mass of the projectile

Initial velocity

## Step 2: Explanation (Part a)

Let's find the acceleration for component and :

According to Newton's law, the power exerted on a object creates its accelerates and this force equal to the mass:

Therefore,

## Step 3: Calculate the final velocity (Part a)

Let's compute the final velocity as follow:

For the horizontal component:

## Step 4: Calculate for the vertical component (Part a)

For the vertical component:

Place the and values in the given equation:

Therefore,

## Step 6: Final Answer (Part a)

The projectile's speed at is .

## Step 7: Given Information (Part b)

We are given the force in two dimensions in the form

.

## Step 8: Explanation (Part b)

Let's apply the equation of horizontal component to find the time:

Simplify,

## Step 8: Final Answer (Part b)

The projectile moving parallel to the axis at .