Question

A body is projected with a velocity v and angle theta upward from horizontal . prove that the trajactory is parabolic

Answer 1

hey!!
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x motion: There is no force in x direction. Therefore , x motion is motion with uniform velocity. In the present problem ,it ( velocity) is v.

The displacement in x direction in time t is

x=vt…………………………………………………..(1)

Now, y motion: for this motion initial velocity is zero. There is acceleration due to gravity in the negative y direction. Then, displacement in y direction is

y=-(1/2)gt^2………………………………………..(2)

Now, we are interested in trajectory that is relation between x and y. Therefore ,we have to eliminate t from eq.(1) and eq.(2).

From eq.(1), t^2=(x/v)^2

Putting this value of t^2 in eq.(2), we get

y =-(1/2)gx^2/v^2……………………………………(3)

Since, g and v are constant. the equation is of the form

y=-ax^2, which is equation of parabola passing through origin and falling in fourth quadrant .

Hence, trajectory in the present problem is a parabola.


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