MCQ
A particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be
- AA straight line
- BAn arc of a circle
- ✓A parabola
- DAn ellipse
✓
Answer
Correct option: C.
A parabola
c
(c) A particle moves with constant acceleration in a direction different from initial
(c) A particle moves with constant acceleration in a direction different from initial
velocity. Let the velocity be $v,$ acceleration be $a,$ angle between them is $\theta\left[\theta<90^{0}\right]$
Component of Velocity in the Direction of $a$ is $v \cos \theta$ and in a direction perpendicular to $a$ is vsin $\theta$
From equations of Kinematics, In the direction of acceleration, $y=v \cos \theta t+\frac{1}{2} a t^{2}-----(1)$
In the direction perpendicular to acceleration,
$x=v \sin \theta t$
$t=\frac{x}{v \sin \theta}--------(2)$
Substituting 2 in $1,$ we get:
$y=v \cos \theta\left(\frac{x}{v \sin \theta}\right)+\frac{1}{2} a\left(\frac{x^{2}}{\sin ^{2} \theta}\right)$
$y=\frac{x}{\tan \theta}+\frac{1}{2} a \frac{x^{2}}{\sin ^{2} \theta}$
This is in the form of a parabola: $y=A x^{2}+B x+C$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In which of the following graphs, the total change in momentum is zero?
A cyclist riding the bicycle at a speed of $14 \sqrt{3} \,m / s$ takes a turn around a circular road of radius $20 \sqrt{3} \,m$ without skidding. What is his inclination to the vertical?
→A projectile is thrown with velocity $u$ making angle $\theta$ with vertical. It just crosses the tops of two poles each of height $h$ after $1\,s$ and $3\,s$, respectively. The maximum height of projectile is ............ $m$
→Two carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat at $T_{1}$ and rejects heat to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by engine $A$ and rejects heat to the sink at ${T}_{3}$. When workdone in both the cases is equal, the value of ${T}$ is
→Two trains, each $50 \,m$ long are travelling in opposite direction with velocity $10 \,m/s$ and $15 \,m/s$. The time of crossing is...........$s$
→In rear-wheel drive cars, the engine rotates the rear wheels and the front wheels rotate only because the car moves. If such a car accelerates on a horizontal road, the friction:
- On the rear wheels is in the forward direction.
- On the front wheels is in the backward direction.
- On the rear wheels has larger magnitude than the friction on the front wheels.
- On the car is in the backward direction.
A particle of mass $1g$ moving with a velocity $\text{v}_1=3\hat{\text{i}}-2\hat{\text{j}}\text{ms}^{-1}$ experiences a perfectly elastic collision with another particle of mass $2g$ and velocity $\text{v}_2=4\hat{\text{j}}-6\hat{\text{k}}\text{ms}^{-1}$. The velocity of the particle is:
→What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $10\,cm$ ($g = 9.8\, m/s^2$) ..... $m/s$
→The following four wires are made of same material. Which one will have the largest elongation when subjected to the same tension ?
The average kinetic energy of hydrogen molecules at $300 K$ is $E.$ At the same temperature, the average kinetic energy of oxygen molecules will be
→