Question

A particle is (X-Y) palne such that it's velocity is given by V=vi+xj where (i and j are vector).the equation of it's trajectory is...

Answer 1

Answer on Question 48682, Physics, Mechanics | Kinematics | Dynamics

Question:

A particle is (X-Y) plane such that it's velocity is given by $V = v_i + x_j$ where $i$ and $j$ are vector. The equation of it's trajectory is?

Solution:

First, we find the projections of particle on axis $x$ and $y$ , respectively:

$$x = v _ {x} t,$$ $$y = v _ {y} t.$$

where $v_{x}$ and $v_{y}$ is the projections of velocity of particle on axis $x$ and $y$ , $t$ is the time. From the conditions of the problem we know that:

$$v _ {x} = v,$$ $$v _ {y} = x.$$

Substituting $v_{x}$ and $v_{y}$ to the formula for projections of particle on axis $x$ and $y$ we obtain:

$$x = v t,$$ $$y = x t.$$

Finally, we obtain equation of particle trajectory: $x = vt$ , $y = vt^2$ .

Answer:

The equation of particle trajectory is $x = vt$ , $y = vt^2$ .

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