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Q.38

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 200

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Short Answer

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 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 .

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