A particle moves in the xy plane with a const | vedclass

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

Question

(D) Given that the particle has acceleration only in the negative $y$-direction,the acceleration in the $x$-direction is $a_x = 0$. Since $a_x = 0$,th

Vedclass · Accepted Answer

All of the above

Vedclass · Answer

(D) Given that the particle has acceleration only in the negative $y$-direction,the acceleration in the $x$-direction is $a_x = 0$. Since $a_x = 0$,the $x$-component of velocity $v_x$ is constant.From the equation $y = ax - bx^2$,differentiate with respect to time $t$: $\frac{dy}{dt} = a\frac{dx}{dt} - 2bx\frac{dx}{dt}$,which gives $v_y = v_x(a - 2bx)$.Differentiating again with respect to time: $\frac{d^2y}{dt^2} = a\frac{d^2x}{dt^2} - 2b\left[\left(\frac{dx}{dt}ight)^2 + x\frac{d^2x}{dt^2}ight]$.Since $a_x = 0$ and $a_y = -g$,we get $-g = -2bv_x^2$,which implies $v_x = \sqrt{\frac{g}{2b}}$.At the origin $(x = 0)$,$v_y = a v_x = a\sqrt{\frac{g}{2b}}$.The angle $	heta$ with the $x$-axis is given by $	an 	heta = \frac{v_y}{v_x} = \frac{a v_x}{v_x} = a$,so $	heta = 	an^{-1}(a)$.Thus,all statements are correct.

$(A)$ Range	$(i)$ $\frac{P}{Q}$
$(B)$ Maximum height	$(ii)$ $P$
$(C)$ Time of flight	$(iii)$ $\frac{P^2}{4 Q}$
$(D)$ Tangent of projection	$(iv)$ $\left(\sqrt{\frac{2}{g Q}}\right) P$

$A$ particle moves in the $xy$ plane with a constant acceleration $g$ in the negative $y$-direction. Its equation of motion is $y = ax - bx^2$,where $a$ and $b$ are constants. Which of the following are correct?

Similar Questions

$A$ projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3 \, ms^{-2}$ for $0.5 \, minutes$. If the maximum height reached by it is $80 \, m$,then the angle of projection is (Take $g = 10 \, ms^{-2}$)

An object is projected such that it attains maximum range. Another body is projected to reach maximum height. If both objects reach the same maximum height,what is the ratio of their initial velocities?

Vedclass Test Series

Exam Paper Generator

Online Exam Module