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Kinematics-2D

362 Questions Start Errorless Test
All Exams Allen Advance Errorless
Q226 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A boy throws a ball with a velocity u at an angle $\alpha$ with the vertical. At the same instant he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of
A.
$u \cos \alpha$
B.
$u \sin \alpha$
C.
$u \tan \alpha$
D.
$\sqrt{u^{2} \tan \alpha}$
Q227 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A projectile is thrown with an initial velocity of $\left(a\hat{i} + b\hat{j}\right)\mathrm{ms}^{-1}$ . If the range of the projectile is twice the maximum height reached by it, then
A.
$a = 2b$
B.
$b = a$
C.
$b = 2a$
D.
$b = 4a$
Q228 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Time taken by the projectile to reach from $A$ to $B$ is $t$ . Then the distance $AB$ is equal to
A.
$\frac{ut}{\sqrt{3}}$
B.
$\frac{\sqrt{3}ut}{2}$
C.
$\sqrt{3} ut$
D.
$2ut$
Q229 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A stone is projected from a horizontal plane. It attains maximum height H and strikes a stationary smooth wall and falls on the ground vertically below the maximum height. Assume the collision to be elastic, the height of the point on the wall where stone will strike is
A.
$\frac{H}{2}$
B.
$\frac{H}{4}$
C.
$\frac{3H}{4}$
D.
$\frac{H}{3}$
Q230 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A circular disc of radius $r = 5 \, \text{m}$ is rotating in horizontal plane about $y$ -axis. $Y$ -axis is vertical axis passing through the centre of disc and $x-z$ is the horizontal plane at ground. The height of disc above ground is $h = 5 \, \text{m}$ . Small particles are ejecting from disc in horizontal direction with speed $12 \, \text{ms}^{-1}$ from the circumference of disc then the distance of these particles from origin when they hits the $x-z$ plane is
A.
$12 \, \text{m}$
B.
$13 \, \text{m}$
C.
$5 \, \text{m}$
D.
$6 \, \text{m}$
Q231 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation $\frac{5\pi}{36}$ radians should strike a given target. In actual practice it was found that a hill just prevented in the trajectory. At what angle of elevation should the gun be fired to hit the target.
A.
$\frac{5\pi}{36}$ radians
B.
$\frac{11\pi}{36}$ radians
C.
$\frac{7\pi}{36}$ radians
D.
$\frac{13\pi}{36}$ radians
Q232 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body is thrown with speed of $30 \, ms^{-1}$ at angle $30^{\circ}$ with horizontal from a perfectly inelastic horizontal floor. The time after which it is moving perpendicular to its initial direction of motion is
A.
6 s
B.
3 s
C.
1.5 s
D.
never
Q233 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body is thrown from a point with speed $50 \, ms^{-1}$ at an angle $37^{\circ}$ with horizontal. When it has moved a horizontal distance of 80 m then its distance from point of projection is
A.
40 m
B.
$40\sqrt{2}$ m
C.
$40\sqrt{5}$ m
D.
None of these
Q234 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A ball is thrown from ground level so as to just clear a wall 4 meters high at a distance of 4 meters and falls at a distance of 14 meters from the wall, then the magnitude of the velocity of the ball is
A.
$\sqrt{281}$ ms $^{-1}$
B.
$\sqrt{812}$ ms $^{-1}$
C.
$\sqrt{182}$ ms $^{-1}$
D.
$\sqrt{128}$ ms $^{-1}$
Q235 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
An object is thrown at an angle $\alpha$ to the horizontal $(0^{\circ} < \alpha < 90^{\circ})$ with a velocity. Then during ascent (ignoring air drag) the acceleration
A.
with which the object moves is $\vec{g}$ , at all points.
B.
tangential to the path decreases.
C.
normal to the path increases, becoming equal to $g$ at the highest point.
D.
All of these
Q236 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A projectile is thrown with a velocity of $20 \, ms^{-1}$ , at an angle of $60^\circ$ with the horizontal. After how much time the velocity vector will make an angle of $45^\circ$ with the horizontal? (Take $g = 10 \, ms^{-2}$ )
A.
$\sqrt{3} \, s$
B.
$\frac{1}{\sqrt{3}} \, s$
C.
$(\sqrt{3} + 1) \, s$
D.
$(\sqrt{3} - 1) \, s$
Q237 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A golfer standing on level ground hits a ball with a velocity of $u = 52 \, ms^{-1}$ at an angle $\theta$ above the horizontal. If $\tan\theta = \frac{5}{12}$ , then the time for which the ball is at least 15 m above the ground (i.e. between A and B) will be (take $g = 10 \, ms^{-2}$ )
A.
1 s
B.
2 s
C.
3 s
D.
4 s
Q238 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Which of the following ideas is helpful in understanding projectile motion?
A.
$v_{x}^{2} + v_{y}^{2} = constant$
B.
Acceleration is +g when the object is rising and -g when falling
C.
In the absence of friction the trajectory will depend on the object's mass as well as its initial velocity and launch angle
D.
The horizontal motion is independent of the vertical motion
Q239 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A ball is projected upwards from the top of the tower with a velocity $50 \, ms^{-1}$ making an angle $30^{\circ}$ with the horizontal. The height of tower is 70 m. After how many seconds the ball will strike the ground?
A.
3 s
B.
5 s
C.
7 s
D.
9 s
Q240 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The equation of projectile is $y = \sqrt{3}x - \frac{g}{2}x^{2}$ . The angle of projection and initial velocity is
A.
$30^{\circ}$ , $4\ ms^{-1}$
B.
$60^{\circ}$ , $2\ ms^{-1}$
C.
$60^{\circ}$ , $4\ ms^{-1}$
D.
$90^{\circ}$ , $4\ ms^{-1}$
Q241 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80~\mathrm{ms}^{-1}$ . Its time of flight is $T$ . Its velocity at $t = \frac{T}{4}$ has a magnitude of nearly
A.
$200~\mathrm{ms}^{-1}$
B.
$300~\mathrm{ms}^{-1}$
C.
$140~\mathrm{ms}^{-1}$
D.
$100~\mathrm{ms}^{-1}$
Q242 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle is projected from a point $A$ with velocity $u\sqrt{2}$ at an angle of $45^{\circ}$ with horizontal as shown in figure. It strikes the plane $BC$ at right angles. The velocity of the particle at the time of collision is:
A.
$\frac{\sqrt{3}u}{2}$
B.
$\frac{u}{2}$
C.
$\frac{2u}{\sqrt{3}}$
D.
$u$
Q243 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Consider a boy on a trolley who throws a ball with speed $20 \, ms^{-1}$ at an angle $37^{\circ}$ with respect to trolley in direction of motion of trolley which moves horizontally with speed $10 \, ms^{-1}$ then what will be maximum distance travelled by ball parallel to road
A.
20.2 m
B.
12 m
C.
31.2 m
D.
62.4 m
Q244 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A projectile is thrown at angle $\beta$ with vertical. It reaches a maximum height $H$ . The time taken to reach highest point of its path is
A.
$\sqrt{\frac{H}{g}}$
B.
$\sqrt{\frac{2H}{g}}$
C.
$\sqrt{\frac{H}{2g}}$
D.
$\sqrt{\frac{2H}{g\cos\beta}}$
Q245 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body is projected at angle $45^{\circ}$ to horizontal with velocity $20 \, ms^{-1}$ from ground. If there is an acceleration in horizontal direction of $2 \, ms^{-2}$ , then calculate horizontal range of this particle
A.
40 m
B.
48 m
C.
8 m
D.
20 m
Q246 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle is projected with a velocity of $20 \, ms^{-1}$ at an angle of $30^{\circ}$ to an inclined plane of inclination $30^{\circ}$ to the horizontal. The particle hits the inclined plane at an angle $30^{\circ}$ , during its journey. The time of flight is
A.
$\frac{20\sin(60^{\circ})}{g}$
B.
$\frac{20\sin(60^{\circ})}{g\cos(30^{\circ})}$
C.
$\frac{20\sin(30^{\circ})}{g\cos(60^{\circ})}$
D.
$\frac{20\sin(30^{\circ})}{g}$
Q247 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle starts flying in the $xy$ -plane with a speed of $2\hat{i} + 5x\hat{j}$ . Initial position of the particle was the origin $(0, 0)$ of the plane. The trajectory of the particle is represented by the equation
A.
$y = 1.25x^2$
B.
$y = 5x^2$
C.
$y = 2.5x^2$
D.
$x = 5y^2$
Q248 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The ceiling of a tunnel is 5 m high. What is the maximum horizontal distance that a ball thrown with a speed of $20 \, ms^{-1}$ , can go without hitting the ceiling of the tunnel? (Take $g = 10 \, ms^{-2}$ )
A.
30 m
B.
40 m
C.
$30\sqrt{2} \, m$
D.
$20\sqrt{3} \, m$
Q249 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In projectile motion, the modulus of rate of change of speed
A.
is constant
B.
first increases then decreases
C.
first decreases then increases
D.
None of these
Q250 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
If a stone is to hit at a point which is at a horizontal distance d away and at a height h above the point from where the stone starts, then what is the value of initial speed u if the stone is launched at an angle $\theta$ ?
A.
$\frac{g}{\cos\theta}\sqrt{\frac{d}{2(d\tan\theta - h)}}$
B.
$\frac{d}{\cos\theta}\sqrt{\frac{g}{2(d\tan\theta - h)}}$
C.
$\sqrt{\frac{gd^2}{h\cos^2\theta}}$
D.
$\sqrt{\frac{gd^2}{d - h}}$