A particle moves in a plane with constant acc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) particle moves with constant acceleration in a direction different from the initial velocity. Let the initial velocity be $v$ and the constant acc

Vedclass · Accepted Answer

$A$ parabola

Vedclass · Answer

(C) particle moves with constant acceleration in a direction different from the initial velocity. Let the initial velocity be $v$ and the constant acceleration be $a$,with an angle $	heta$ between them $(0 Resolve the velocity into two components: one parallel to the acceleration $(v \cos 	heta)$ and one perpendicular to the acceleration $(v \sin 	heta)$.Let the direction perpendicular to the acceleration be the $x$-axis and the direction of acceleration be the $y$-axis.In the $x$-direction,there is no acceleration,so the displacement is $x = (v \sin 	heta) t$,which gives $t = \frac{x}{v \sin 	heta}$.In the $y$-direction,the initial velocity is $v \cos 	heta$ and the acceleration is $a$. The displacement is $y = (v \cos 	heta) t + \frac{1}{2} a t^2$.Substituting the expression for $t$ into the equation for $y$:$y = (v \cos 	heta) \left( \frac{x}{v \sin 	heta} ight) + \frac{1}{2} a \left( \frac{x}{v \sin 	heta} ight)^2$$y = x \cot 	heta + \frac{a}{2 v^2 \sin^2 	heta} x^2$.This equation is of the form $y = Ax^2 + Bx$,which represents a parabola.

$A$ particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be

Similar Questions

At which points of its trajectory will a projectile have minimum and maximum speed?

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \, m$. With the same effort,he throws the ball vertically upwards. The maximum height attained by the ball is ......... $m$.

$A$ shell is fired vertically upwards with a velocity $v_1$ from a trolley moving horizontally with velocity $v_2$. $A$ person on the ground observes the motion of the shell as a parabola,whose horizontal range is ....

An object is projected from the ground with speed $u$ at an angle $\theta$ with the horizontal. The radius of curvature of its trajectory at the maximum height from the ground is ..........

The equations of motion of a projectile are given by $x = 36t$ metre and $2y = 96t - 9.8t^2$ metre. The angle of projection is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module