Kinematics-2D
384 Questions
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Q326
Objective
Taking it together
MCQ
A particle moves along a parabolic path $y = -9x^{2}$ in such a way that the x-component of velocity remains constant and has a value $1/3 \, ms^{-1}$ . The acceleration of the particle is
A.
$\frac{1}{3} \, ms^{-2}$
B.
$3 \, ms^{-2}$
C.
$\frac{2}{3} \, ms^{-2}$
D.
$2 \, ms^{-2}$
Q327
Objective
Taking it together
MCQ
A projectile can have same range from two angles of projection with same initial speed. If $h_{1}$ and $h_{2}$ be the maximum heights, then
A.
$R = \sqrt{h_{1} h_{2}}$
B.
$R = \sqrt{2 h_{1} h_{2}}$
C.
$R = 2\sqrt{h_{1} h_{2}}$
D.
$R = 4\sqrt{h_{1} h_{2}}$
Q328
Objective
Taking it together
MCQ
A ball is projected from ground with a speed of $20 \, ms^{-1}$ at an angle of $45^{\circ}$ with horizontal. There is a wall of 25 m height at a distance of 10 m from the projection point. The ball will hit the wall at a height of
A.
5 m
B.
7.5 m
C.
10 m
D.
12.5 m
Q329
Objective
Taking it together
MCQ
A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be
A.
$20\sqrt{2}$ m
B.
10 m
C.
$10\sqrt{2}$ m
D.
20 m
Q330
Objective
Taking it together
MCQ
At the height 80 m, an aeroplane is moving with $150 \, ms^{-1}$ . A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? (Take, $g = 10 \, ms^{-2}$ )
A.
605.3 m
B.
600 m
C.
80 m
D.
230 m
Q331
Objective
Taking it together
MCQ
A ball is projected upwards from the top of a tower with velocity $25 \, ms^{-1}$ making an angle of $30^\circ$ with the horizontal. If the height of the tower is 70 m, after what time from the instant of throwing, will the ball reach the ground? (Take, $g = 10 \, ms^{-2}$ )
A.
2 s
B.
5 s
C.
7 s
D.
9 s
Q332
Objective
Taking it together
MCQ
From the top of a tower of height 40 m, a ball is projected upwards with a speed of $20 \, ms^{-1}$ at an angle of elevation of $30^\circ$ . The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (Take, $g = 10 \, ms^{-2}$ )
A.
2:1
B.
3:1
C.
3:2
D.
1.5:1
Q333
Objective
Taking it together
MCQ
The coordinates of a moving particle at any time t are given by x = ct and $y = bt^{2}$ . The speed of the particle is given by
A.
$2t\sqrt{b^{2}-c^{2}}$
B.
$\sqrt{4b^{2}t^{2}+c^{2}}$
C.
$2t(b+c)$
D.
$2t(b-c)$
Q334
Objective
Taking it together
MCQ
A ball rolls off the edge of a horizontal table top 4 m high. If it strikes the floor at a point 5 m horizontally away from the edge of the table, what was its speed at the instant it left the table?
A.
$2.5 \, ms^{-1}$
B.
$3.5 \, ms^{-1}$
C.
$5.55 \, ms^{-1}$
D.
$6.5 \, ms^{-1}$
Q335
Objective
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MCQ
A ball is thrown from the ground to a wall 3 m high at a distance of 6 m and falls 18 m away from the wall, the angle of projection of ball is
A.
$\tan^{-1}\left(\frac{3}{2}\right)$
B.
$\tan^{-1}\left(\frac{2}{3}\right)$
C.
$\tan^{-1}\left(\frac{1}{2}\right)$
D.
$\tan^{-1}\left(\frac{3}{4}\right)$
Q336
Objective
Taking it together
MCQ
The horizontal range and maximum height attained by a projectile are R and H, respectively. If a constant horizontal acceleration a = g/4 is imparted to the projectile due to wind, then its horizontal range and maximum height will be
A.
$(R + H), \frac{H}{2}$
B.
$\left(R + \frac{H}{2}\right), 2H$
C.
$(R + 2H), H$
D.
$(R + H), H$
Q337
Objective
Taking it together
MCQ
An object is projected with a velocity of $20 \, ms^{-1}$ making an angle of $45^{\circ}$ with horizontal. The equation for trajectory is $h = Ax - Bx^{2}$ , where h is height, x is horizontal distance, A and B are constants. The ratio A : B is (Take, $g = 10 \, ms^{-2}$ )
A.
1:5
B.
5:1
C.
1:40
D.
40:1
Q338
Objective
Taking it together
MCQ
If the instantaneous velocity of a particle projected as shown in figure is given by $\mathbf{v} = a\hat{\mathbf{i}} + (b - ct)\hat{\mathbf{j}}$ . where $a, b$ and $c$ are positive constants, the range on the horizontal plane will be
A.
2ab/c
B.
ab/c
C.
ac/b
D.
a/2bc
Q339
Objective
Taking it together
MCQ
Two particles are simultaneously projected in opposite directions horizontally from a given point in space, where gravity g is uniform. If $u_{1}$ and $u_{2}$ be their initial speeds, then the time t after which their velocities are mutually perpendicular is given by
A.
$\frac{\sqrt{u_{1}u_{2}}}{g}$
B.
$\frac{\sqrt{u_{1}^{2}+u_{2}^{2}}}{g}$
C.
$\frac{\sqrt{u_{1}(u_{1}+u_{2})}}{g}$
D.
$\frac{\sqrt{u_{2}(u_{1}+u_{2})}}{g}$
Q340
Objective
Taking it together
MCQ
A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80 \, ms^{-1}$ . Its time of flight is T. Its velocity at t = T/4 has a magnitude of nearly
A.
$200 \, ms^{-1}$
B.
$300 \, ms^{-1}$
C.
$100 \, ms^{-1}$
D.
None of these
Q341
Objective
Taking it together
MCQ
A projectile is thrown with some initial velocity at an angle $\alpha$ to the horizontal. Its velocity when it is at the highest point is $(2/5)^{1/2}$ times the velocity when it is at height half of the maximum height. Find the angle of projection $\alpha$ with the horizontal.
A.
$30^{\circ}$
B.
$45^{\circ}$
C.
$60^{\circ}$
D.
$37^{\circ}$
Q342
Objective
Taking it together
MCQ
A very broad elevator is going up vertically with a constant acceleration of $2 \, ms^{-2}$ . At the instant when its velocity is $4 \, ms^{-1}$ , a ball is projected from the floor of the lift with a speed of $4 \, ms^{-1}$ relative to the floor at an elevation of $30^\circ$ . The time taken by the ball to return the floor is (Take, $g = 10 \, ms^{-2}$ )
A.
$\frac{1}{2} \, s$
B.
$\frac{1}{3} \, s$
C.
$\frac{1}{4} \, s$
D.
$1 \, s$
Q343
Objective
Taking it together
MCQ
A grasshopper can jump a maximum distance of 1.6 m. How far can it go in 10 s?
A.
$5\sqrt{2}$ m
B.
$10\sqrt{2}$ m
C.
$20\sqrt{2}$ m
D.
$40\sqrt{2}$ m
Q344
Objective
Taking it together
MCQ
A body of mass 1kg is projected with velocity $50 \, ms^{-1}$ at an angle of $30^{\circ}$ with the horizontal. At the highest point of its path, a force 10 N starts acting on body for 5 s vertically upward besides gravitational force. What is the horizontal range of the body? (Take, $g = 10 \, ms^{-2}$ )
A.
$125\sqrt{3} \, m$
B.
$200\sqrt{3} \, m$
C.
$500 \, m$
D.
$250\sqrt{3} \, m$
Q345
Objective
Taking it together
MCQ
A projectile is thrown at an angle $\theta$ such that it is just able to cross a vertical wall at its highest point as shown in the figure.
The angle $\theta$ at which the projectile is thrown is given by
A.
$\tan^{-1}\left(\frac{1}{\sqrt{3}}\right)$
B.
$\tan^{-1}\sqrt{3}$
C.
$\tan^{-1}\left(\frac{2}{\sqrt{3}}\right)$
D.
$\tan^{-1}\left(\frac{\sqrt{3}}{2}\right)$
Q346
Objective
Taking it together
MCQ
A jet aeroplane is flying at a constant height of 2 km with a speed $360 \, kmh^{-1}$ above the ground towards a target and releases a bomb. After how much time, it will hit the target and what will be the horizontal distance of the aeroplane from the target, so that the bomb should hit the target? (Take, $g = 10 \, ms^{-2}$ )
A.
10 s, 1 km
B.
20 s, 2 km
C.
30 s, 3 km
D.
40 s, 4 km
Q347
Objective
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MCQ
Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance 120 m. Which of the following is true?
A.
The two balls can never meet
B.
The balls can meet, if the ball $B$ is thrown 1 s later
C.
The two balls meet at a height of $45\mathrm{m}$
D.
None of the above
Q348
Objective
Taking it together
MCQ
Two particles are projected from the same point with same speed $u$ at angles of projection $\alpha$ and $\beta$ from horizontal. The maximum heights attained by them are $h_1$ and $h_2$ respectively, $R$ is the range for both. If $t_1$ and $t_2$ are their times of flight respectively, then which amongst the option(s) is/are incorrect?
A.
$\alpha + \beta = \frac{\pi}{2}$
B.
$R = 4\sqrt{h_1h_2}$
C.
$\tan \alpha = \frac{t_1}{t_2} = \sqrt{h_1h_2}$
D.
$\tan \alpha = \frac{h_1}{h_2}$
Q349
Objective
Taking it together
MCQ
A particle is projected from the ground at an angle $\theta$ with the horizontal with an initial speed u. Time after which velocity vector of the projectile is perpendicular to the initial velocity.
A.
$u/g \sin\theta$
B.
$u/g \cos\theta$
C.
$2u/g \sin\theta$
D.
$2u \tan\theta$
Q350
Objective
Taking it together
MCQ
A particle is projected from horizontal making an angle of $53^{\circ}$ with initial velocity of $100 \, ms^{-1}$ . The time taken by the particle to make angle $45^{\circ}$ from horizontal is
A.
14 s
B.
2 s
C.
Both
D.
None of these
