What do you mean by projectile motion and projectile particle ? Find the value of the position of a projectile particle at any instant of time.
What do you mean by projectile motion and projectile particle ? Find the value of the position of a projectile particle at any instant of time.
When an object is thrown in gravitational field of the Earth, it moves with constant horizontal velocity and constant vertical acceleration. Such a two dimensional motion is called a projectile motion and such an object is called a projectile.
For example, when we kick a football, it performs projectile motion if air resistance is neglected. A projectile has motion along horizontal path with uniform velocity.
A projectile has motion along vertical path under gravity with uniform acceleration equal to ' $g$ '.
Suppose that the projectile is launched with velocity $\vec{v}_{0}$ that makes an angle $\theta_{0}$ with the $\mathrm{X}$-axis as show in figure.
$\mathrm{g}$ acts on the body along ' $\mathrm{Y}$ ' axis and in opposite direction
The acceleration ' $a$ ' is given by
$\therefore \vec{a}=-\mathrm{g} \hat{j}$
here $a_{x}=0, a_{y}=-g$
The velocity $\vec{v}_{0}$ can be divided into two components,
$v_{\mathrm{o} x}=v_{\mathrm{o}} \cos \theta_{\mathrm{o}}$
$v_{\mathrm{oy}}=v_{\mathrm{o}} \sin \theta_{\mathrm{o}}$
If we take the initial position to be the origin of the coordinate system, the coordinates of the point of projection would be :
$x_{0}=0$, and $y_{0}=0$
Similar Questions
The position of a particle is given by
$r =3.0 t \hat{ i }-2.0 t^{2} \hat{ j }+4.0 \hat{ k } \;m$
where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.
$(a)$ Find the $v$ and a of the particle?
$(b)$ What is the magnitude and direction of velocity of the particle at $t=2.0 \;s ?$
The position of a particle is given by
$r =3.0 t \hat{ i }-2.0 t^{2} \hat{ j }+4.0 \hat{ k } \;m$
where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.
$(a)$ Find the $v$ and a of the particle?
$(b)$ What is the magnitude and direction of velocity of the particle at $t=2.0 \;s ?$
At time $t =0$ a particle starts travelling from a height $7\,\hat{z} cm$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $x$ and $y$ directions are defined as $3\,t$ and $5\,t^{3}$ respectively. At $t =1\,s$ acceleration of the particle will be.
At time $t =0$ a particle starts travelling from a height $7\,\hat{z} cm$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $x$ and $y$ directions are defined as $3\,t$ and $5\,t^{3}$ respectively. At $t =1\,s$ acceleration of the particle will be.
- [JEE MAIN 2022]
A man moves in an open field such that after moving $10 \,m$ on a straight line, he makes a sharp turn of $60^{\circ}$ to his left. The total displacement just at the start of $8^{\text {th }}$ turn is equal to ........$m$
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