Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q48PE (page 124)

Prove that the trajectory of a projectile is parabolic, having the form y=ax+bx2. To obtain this expression, solve the equation x=voxtfor and substitute it into the expression for y=voyt1(1/2)gt2(These equations describe the xand y positions of a projectile that starts at the origin.) You should obtain an equation of the form y=ax+bx2where a and bare constants.

Short Answer

Expert verified

The trajectory of the displacement is proved to be a parabolic path.

When gravity first exerts force on an item, its initial velocity indicates how fast it travels. The final velocity, on the other hand, is a vector number that measures a moving body's speed and direction after it has reached its maximum acceleration.

Step by step solution

01

Definition of initial velocity

The velocity can be said as.vi The velocity is making some angle with the x axis.

In the x frame the acceleration are zero, hence the velocity in the x frame will be constant.

02

Proving parabolic trajectory of displacement

The initial velocity and the final velocity and the average velocity will be the same.

V¯=Xtt=XVicosθ.......1

Now let’s calculate the displacement.

Hence the trajectory of the displacement is proved to be a parabolic path.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Gun sights are adjusted to aim high to compensate for the effect of

gravity, effectively making the gun accurate only for a specific range.

(a) If a gun is sighted to hit targets that are at the same height as the gun and100.0m away, how low will the bullet hit if aimed directly at a target 150.0m away? The muzzle velocity of the bullet is275m/s.

(b) Discuss qualitatively how a larger muzzle velocity would affect this problem and what would be the effect of air resistance.

Derive R=Vo2sin2θogfor the range of a projectile on level ground by finding the time at which becomes zero and substituting this value of into the expression forX1X0 , noting that R=X1X0.

Suppose you first walk 12.0 m in a direction 20º west of north and then 20.0 m in a direction 40.0º south of west. How far are you from your starting point and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , as in Figure 3.56, then this problem finds their sum R = A + B.)

An owl is carrying a mouse to the chicks in its nest. Its position at that

time is 4.00 m west and 12.0 m above the center of the 30.0 cm diameter nest. The owl is flying east at 3.50 m/s at an angle30.0ºbelow the horizontal when it accidentally drops the mouse. Is the owl lucky enough to have the mouse hit the nest? To answer this question, calculate the horizontal position of the mouse when it has fallen 12.0 m.

A cloud of dirt falls from the bed of a moving truck. It strikes the ground directly below the end of the truck. What is the direction of its velocity relative to the truck just before it hits? Is this the same as the direction of its velocity relative to ground just before it hits? Explain your answers.
See all solutions

Recommended explanations on Physics Textbooks

Electrostatics

Read Explanation

Fundamentals of Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Energy Physics

Read Explanation

Electricity

Read Explanation

Wave Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free