Kinematics-2D
384 Questions
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Q301
Objective
Taking it together
MCQ
If time of flight of a projectile is 10 s. Range is 500 m. The maximum height attained by it will be
A.
125 m
B.
50 m
C.
100 m
D.
150 m
Q302
Objective
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MCQ
A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with velocity v. While rising up the velocity of the mass after t seconds will be
A.
$\sqrt{(v\cos\theta)^{2}+(v\sin\theta)^{2}}$
B.
$\sqrt{(v\cos\theta-v\sin\theta)^{2}-gt}$
C.
$\sqrt{v^{2}+g^{2}t^{2}-(2v\sin\theta)gt}$
D.
$\sqrt{v^{2}+g^{2}t^{2}-(2v\cos\theta)gt}$
Q303
Objective
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MCQ
A stone is thrown at an angle $\theta$ with the horizontal, reaches a maximum height $H$ . Then, the time of flight of stone will be
A.
$\sqrt{\frac{2H}{g}}$
B.
$2\sqrt{\frac{2H}{g}}$
C.
$\frac{2\sqrt{2H\sin\theta}}{g}$
D.
$\frac{\sqrt{2H\sin\theta}}{g}$
Q304
Objective
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MCQ
A ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy KE of the ball varies with height h as
A.
B.
C.
D.
Q305
Objective
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MCQ
For a given velocity, a projectile has the same range R for two angles of projection. If $t_{1}$ and $t_{2}$ are the time of flight in the two cases, then $t_{1}t_{2}$ is equal to
A.
$\frac{2R}{g}$
B.
$\frac{R}{g}$
C.
$\frac{4R}{g}$
D.
$\frac{R}{2g}$
Q306
Objective
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MCQ
A cricket ball is hit for a six by the bat at an angle of $45^{\circ}$ to the horizontal with kinetic energy K. At the highest point, the kinetic energy of the ball is
A.
zero
B.
K
C.
K/2
D.
$K/\sqrt{2}$
Q307
Objective
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MCQ
The equation of motion of a projectile is $y = 12x - \frac{3}{4}x^{2}$ What is the range of the projectile?
A.
12 m
B.
16 m
C.
20 m
D.
24 m
Q308
Objective
Taking it together
MCQ
A ball of mass m is projected from the ground with an initial velocity u making an angle of $\theta$ with the vertical. What is the change in velocity between the point of projection and the highest point?
A.
$u \cos \theta$ downward
B.
$u \cos \theta$ upward
C.
$u \sin \theta$ upward
D.
$u \sin \theta$ downward
Q309
Objective
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MCQ
The equation of projectile is $Y = \sqrt{3}X - \frac{1}{2} gX^{2}$ . The velocity of projection is
A.
$1 \, ms^{-1}$
B.
$2 \, ms^{-1}$
C.
$3 \, ms^{-1}$
D.
$1.2 \, ms^{-1}$
Q310
Objective
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MCQ
The range of a projectile when launched at an angle $\theta$ is same as when launched at an angle $2\theta$ . What is the value of $\theta$ ?
A.
$15^{\circ}$
B.
$30^{\circ}$
C.
$45^{\circ}$
D.
$60^{\circ}$
Q311
Objective
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MCQ
A particle is thrown with a speed $u$ at an angle $\theta$ with the horizontal. When the particle makes an angle $\phi$ with the horizontal, its speed changes to $v$ , where
A.
$v = u \cos \theta$
B.
$v = u \cos \theta \cos \phi$
C.
$v = u \cos \theta \sec \phi$
D.
$v = u \sec \theta \cos \phi$
Q312
Objective
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MCQ
A projectile has the maximum range 500 m. If the projectile is thrown up a smooth inclined plane of $30^{\circ}$ with the same (magnitude) velocity, the distance covered by it along the inclined plane till it stops will be
A.
250 m
B.
500 m
C.
750 m
D.
1000 m
Q313
Objective
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MCQ
A projectile $A$ is thrown at an angle $30^{\circ}$ to the horizontal from point $P$ . At the same time, another projectile $B$ is thrown with velocity $v_{2}$ upwards from the point $Q$ vertically below the highest point $A$ would reach. For $B$ to collide with $A$ , the ratio $\frac{v_{2}}{v_{1}}$ should be
A.
$\frac{\sqrt{3}}{2}$
B.
2
C.
$\frac{1}{2}$
D.
$\frac{2}{\sqrt{3}}$
Q314
Objective
Taking it together
MCQ
A ball is thrown from a point O aiming a target at angle $30^{\circ}$ with the horizontal, so that the ball hits the target at B but the ball hits at point A, a vertical distance h below B.
If the initial velocity of the ball is $20 \, ms^{-1}$ and the horizontal distance between O and C is 10 m. Find the value of h.
A.
$\frac{g}{6}\mathrm{m}$
B.
$\frac{g}{10}\mathrm{m}$
C.
$\frac{g}{3}\mathrm{m}$
D.
$\frac{g}{12}\mathrm{m}$
Q315
Objective
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MCQ
A ball is thrown from a point with a speed $v_{0}$ at an angle of projection $\theta$ . From the same point and at the same instant, a person starts running with a constant speed $v_{0}/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
A.
Yes, $60^{\circ}$
B.
Yes, $30^{\circ}$
C.
No
D.
Yes, $45^{\circ}$
Q316
Objective
Taking it together
MCQ
The initial velocity of a particle of mass 2 kg is $(4\hat{\mathbf{i}} + 4\hat{\mathbf{j}})\ \mathrm{ms}^{-1}$ . A constant force of $-20\hat{\mathbf{j}}\ N$ is applied on the particle. Initially, the particle was at $(0, 0)$ . Find the x-coordinate of the point, where its y-coordinate is again zero.
A.
3.2 m
B.
6 m
C.
4.8 m
D.
1.2 m
Q317
Objective
Taking it together
MCQ
An object of mass m is projected with a momentum p at such an angle that its maximum height is 1/4th of its horizontal range. Its minimum kinetic energy in its path will be
A.
$\frac{p^{2}}{8m}$
B.
$\frac{p^{2}}{4m}$
C.
$\frac{3p^{2}}{4m}$
D.
$\frac{p^{2}}{m}$
Q318
Objective
Taking it together
MCQ
The equation of motion of a projectile are given by $x = 36 \, t \, \text{m}$ and $2y = 96 \, t - 9.8 \, t^2 \, \text{m}$ . The angle of projection is
A.
$\sin^{-1} \left( \frac{4}{5} \right)$
B.
$\sin^{-1} \left( \frac{3}{5} \right)$
C.
$\sin^{-1} \left( \frac{4}{3} \right)$
D.
$\sin^{-1} \left( \frac{3}{4} \right)$
Q319
Objective
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MCQ
Two stones are projected so as to reach the same distance from the point of projection on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the height attained by them. Then, angle of projection of the stone which attains smaller height is
A.
$45^{\circ}$
B.
$60^{\circ}$
C.
$30^{\circ}$
D.
$\tan^{-1}(3/4)$
Q320
Objective
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MCQ
An arrow is shot into air. Its range is 200 m and its time of flight is 5 s. If $g = 10 \, ms^{-2}$ , then horizontal component of velocity and the maximum height will be respectively
A.
$20 \, ms^{-1}$ , 62.50 m
B.
$40 \, ms^{-1}$ , 31.25 m
C.
$80 \, ms^{-1}$ , 62.5 m
D.
None of these
Q321
Objective
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MCQ
A body is projected from the ground with a velocity $\mathbf{v} = (3\hat{\mathbf{i}} + 10\hat{\mathbf{j}}) \, \text{ms}^{-1}$ . The maximum height attained and the range of the body respectively are (Take, $g = 10 \, ms^{-2}$ )
A.
5 m and 6 m
B.
3 m and 10 m
C.
6 m and 5 m
D.
3 m and 5 m
Q322
Objective
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MCQ
A cricket fielder can throw the cricket ball with a speed $v_{0}$ . If he throws the ball while running with speed $u$ at an angle $\theta$ to the horizontal, what is the effective angle to the horizontal at which the ball is projected in air as seen by a spectator? [NCERT Exemplar]
A.
$\tan^{-1}\left(\frac{v_{0}\cos\theta}{u + v_{0}\sin\theta}\right)$
B.
$\tan^{-1}\left(\frac{v_{0}\sin\theta}{u + v_{0}\cos\theta}\right)$
C.
$\tan^{-1}\left(\frac{u}{v_{0}\cos\theta + v_{0}\sin\theta}\right)$
D.
$\tan^{-1}\left(\frac{v_{0}\sin\theta + v_{0}\cos\theta}{u}\right)$
Q323
Objective
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MCQ
A particle is projected with a velocity of $30 \, ms^{-1}$ , at an angle of $\theta_{0} = \tan^{-1} \left( \frac{3}{4} \right)$ . After 1 s, the particle is moving at an angle $\theta$ to the horizontal, where $\tan\theta$ will be equal to (Take, $g = 10 \, ms^{-2}$ )
A.
1
B.
2
C.
$\frac{1}{2}$
D.
$\frac{1}{3}$
Q324
Objective
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MCQ
A bomber plane moves horizontally with a speed of $500 \, ms^{-1}$ and a bomb released from it, strikes the ground in 10 s. Angle at which it strikes the ground will be (Take, $g = 10 \, ms^{-2}$ )
A.
$\tan^{-1}\left(\frac{1}{5}\right)$
B.
$\tan^{-1}\left(\frac{1}{2}\right)$
C.
$\tan^{-1}(1)$
D.
$\tan^{-1}(5)$
Q325
Objective
Taking it together
MCQ
Two balls are thrown simultaneously from ground with same velocity of $10 \, ms^{-1}$ but different angles of projection with horizontal. Both balls fall at same distance $5\sqrt{3} \, m$ from point of projection. What is the time interval between balls striking the ground?
A.
$(\sqrt{3}-1) \, s$
B.
$(\sqrt{3}+1) \, s$
C.
$\sqrt{3} \, s$
D.
$1 \, s$