   Chapter 13.4, Problem 32E

Chapter
Section
Textbook Problem

# A ball with mass 0.8 kg is thrown southward into the air with a speed of 30 m/s at an angle of 30° to the ground. A west wind applies a steady force of 4 N to the ball in an easterly direction. Where does the ball land and with what speed?

To determine

To find: Where the ball land and speed of the ball.

Explanation

Given:

m=0.8kg , θ=30° , v0=30ms and F(t)=4N .

Formula:

Write the expression for second law of motion.

F=ma (1)

Here,

F is the force,

m is the mass, and

a is the acceleration.

Write the expression to find the acceleration.

a(t)=v(t)

v(t)=a(t)dt (2)

Write the expression to find the velocity.

v(t)=r(t)

r(t)=v(t)dt (3)

Place the ball at the origin and consider that j is to be pointing in the northward direction with i pointing east and k pointing in upward.

Modify equation (1).

a=Fm

Substitute 4N for F and 0.8kg for m ,

a=40.8=5ms2

The wind applies a constant acceleration of 5ms2 in the eastern direction.

By combining the acceleration due to gravity, the acceleration acting on the ball is a(t)=5i9.8k

Substitute 5i9.8k for a(t) in equation (2),

v(t)=(5i9.8k)dt=5idt9.8kdt

v(t)=5ti9.8tk+v(0) (4)

The general expression for v(0) in terms of j and k is,

v(0)=v0cosθj+v0sinθk .

Substitute 30° for θ and 30ms for v0 ,

v(0)=30cos(30°)j+30sin(30°)k=30(32)j+30(12)k=153j+15k

Substitute 153j+15k for v0 in equation (4),

v(t)=5ti9.8tk+(153j+15k)=5ti9.8tk153j+15k=5ti153j+(159.8t)k

Substitute 5ti153j+(159.8t)k for v(t) in equation (3),

r(t)=(5ti153j+(159.8t)k)dt=5tidt153jdt+15kdt9.8tkdt=5(t22)i153tj+15tk9

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Differentiate. y=x2+1x31

Single Variable Calculus: Early Transcendentals, Volume I

#### In Exercises 1-6, solve for y. (x2)2+(y+1)2=9

Calculus: An Applied Approach (MindTap Course List)

#### Let f be the function defined by f(x)={x2+1ifx0xifx0 Find f(2), f(0), and f(1).

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Problems 33 – 38, solve each inequality. 34.

Mathematical Applications for the Management, Life, and Social Sciences

#### Finding a Derivative In Exercises 81-86, find F'(x). F(x)=xx+2(4t+1)dt

Calculus: Early Transcendental Functions (MindTap Course List)

#### Explain the difference between passive and active deception.

Research Methods for the Behavioral Sciences (MindTap Course List) 