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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炉=Xtt=XVicos胃.......1

Now let鈥檚 calculate the displacement.

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

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