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Kinematics-2D

362 Questions Start Errorless Test
All Exams Allen Advance Errorless
Basic Level Q51 Errorless Time of Flight MCQ
A cricket ball is thrown with a velocity of 15 m/s at an angle of $30^{\circ}$ with the horizontal. The time of flight of the ball will be $(g = 10 \, \text{m/s}^{2})$
A.
1.5 s
B.
2.5 s
C.
3.5 s
D.
4.5 s
Basic Level Q52 Errorless Time of Flight MCQ
If $t_{1}$ be the time taken by a body to clear the top of a building and $t_{2}$ be the time spent in air, then $t_{2}:t_{1}$ will be
A.
1:2
B.
2:1
C.
1:1
D.
1:4
Basic Level Q53 Errorless Time of Flight MCQ
A bomb is fired from a cannon with a velocity of 1000 m/s making an angle of $30^{\circ}$ with the horizontal. What is the time taken by the bomb to reach the highest point
A.
11 sec
B.
23 sec
C.
38 sec
D.
51 sec
Basic Level Q54 Errorless Time of Flight MCQ
Two bullets are fired with horizontal velocities of 50 m/s and 100 m/s from two guns at a height of 19.6 m. Which bullet will strike first
A.
First
B.
Second
C.
Simultaneously
D.
None of these
Basic Level Q55 Errorless Time of Flight MCQ
A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with a speed of 15 $ms^{-1}$ . The time taken by the stone to reach the ground is
A.
10 s
B.
5 s
C.
12 s
D.
15 s
Basic Level Q56 Errorless Time of Flight MCQ
Galileo's experiment showed that if two bodies of unequal masses are dropped from the same height, the time required by them to reach the ground are equal. But if they are thrown vertically upwards with the same initial velocity, the ratio of the time required to reach the ground is equal to
A.
The ratio of their masses
B.
The inverse of the ratio of their masses
C.
One
D.
The product of their masses
Advance Level Q57 Errorless Time of Flight MCQ
A particle is projected with a speed $2\sqrt{gh}$ so that it clears two walls of equal height h which are at a distance 2h from each other. The time taken by the particle to pass between the two walls is
A.
$\sqrt{\frac{2h}{g}}$
B.
$\frac{2h}{g}$
C.
$\sqrt{2}\frac{h}{g}$
D.
$2\sqrt{\frac{h}{g}}$
Advance Level Q58 Errorless Time of Flight MCQ
A projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal direction with a velocity of $147 \, ms^{-1}$ . Then the time after which its inclination with the horizontal is $45^{\circ}$ is
A.
$15 \, s$
B.
$10.98 \, s$
C.
$5.49 \, s$
D.
$2.745 \, s$
Advance Level Q59 Errorless Time of Flight MCQ
A cannon ball is fired with a velocity v in a direction making an angle $\theta$ with the horizontal. At the highest point of its path it breaks into two parts of equal masses. One of the parts retraces the initial path of the ball. The speed of the second part immediately after explosion in m/s will be
A.
$\frac{3}{2}v\cos\theta$
B.
$\sqrt{\frac{3}{2}}v\cos\theta$
C.
$2v\cos\theta$
D.
$3v\cos\theta$
Advance Level Q60 Errorless Time of Flight MCQ
From the top of a tower of height 40 m a ball is projected upwards with a speed of 20 m/s at an angle of elevation of $30^{\circ}$ . Then 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.
4:1
Basic Level Q61 Errorless Horizontal Range MCQ
A projectile fired with initial velocity u at some angle $\theta$ , has a range R. If the initial velocity be doubled at the same angle of projection, then the range will be
A.
2R
B.
R/2
C.
R
D.
4R
Basic Level Q62 Errorless Horizontal Range MCQ
The range of a particle when launched at an angle of $15^{\circ}$ with the horizontal is $1.5 \, km$ . What is the range of the projectile when launched at an angle of $45^{\circ}$ to the horizontal
A.
$1.5 \, km$
B.
$3.0 \, km$
C.
$6.0 \, km$
D.
$0.75 \, km$
Basic Level Q63 Errorless Horizontal Range MCQ
Three identical balls are thrown with same speed at angles of $15^{\circ}$ , $45^{\circ}$ and $75^{\circ}$ with the horizontal respectively. The ratio of their distances from the point of projection to the where they hit the ground will be
A.
$1:\sqrt{2}:1$
B.
$1:2:1$
C.
$2:4:3$
D.
$1:2:\sqrt{3}$
Basic Level Q64 Errorless Horizontal Range MCQ
Five balls A, B, C, D and E are projected with the same speed making angles of $10^{\circ}$ , $30^{\circ}$ , $45^{\circ}$ , $60^{\circ}$ , $80^{\circ}$ respectively with the horizontal. Which ball will strike the ground at the farthest point
A.
B
B.
A
C.
E
D.
C
Basic Level Q65 Errorless Horizontal Range MCQ
An object is thrown along a direction inclined at an angle of $45^{\circ}$ with the horizontal direction. The horizontal range of the particle is equal to
A.
Vertical height
B.
Twice the vertical height
C.
Thrice the vertical height
D.
Four times the vertical height
Basic Level Q66 Errorless Horizontal Range MCQ
A projectile is thrown at an angle of $40^{\circ}$ with the horizontal and its range is $R_{1}$ . Another projectile is thrown at an angle $40^{\circ}$ with the vertical and its range is $R_{2}$ . What is the relation between $R_{1}$ and $R_{2}$
A.
$R_{1} = R_{2}$
B.
$R_{1} = 2R_{2}$
C.
$R_{2} = 2R_{1}$
D.
$R_{1} = 4R_{2}/5$
Basic Level Q67 Errorless Horizontal Range MCQ
It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation of $\frac{5\pi}{36}$ radians should strike a given target. In actual practice it was found that a hill just intervened in the trajectory. At what angle of elevation should the gun be fired to hit the target
A.
$\frac{5\pi}{36}$ rad
B.
$\frac{11\pi}{36}$ rad
C.
$\frac{7\pi}{36}$ rad
D.
$\frac{13\pi}{36}$ rad
Basic Level Q68 Errorless Horizontal Range MCQ
Two particles are projected from the same point with the same speed at different angle $\theta_{1}$ and $\theta_{2}$ to the horizontal. They have the same horizontal range. Their times of flight are $t_1$ and $t_2$ respectively. Then
A.
$\theta_{1} + \theta_{2} = 90^{\circ}$
B.
$\frac{t_1}{t_2} = \frac{\tan\theta_1}{\tan\theta_2}$
C.
$\frac{t_1}{t_2} = \tan\theta_2$
D.
$\frac{t_1}{t_2} = \tan\theta_1$
Basic Level Q69 Errorless Horizontal Range MCQ
A projectile thrown from a height of 10 m with velocity of $\sqrt{2}$ m/s, the projectile will fall, from the foot of projection, at distance ( $g = 10 \, m/s^{2}$ )
A.
1 m
B.
2 m
C.
3 m
D.
$\sqrt{2}$ m
Basic Level Q70 Errorless Horizontal Range MCQ
On throwing a ball from the top of a vertical tower with a horizontal velocity of 20 m/s, it hits the earth at a distance of 50 m from the foot of the tower. If the ball is thrown with the same horizontal velocity from the top of another tower of height four times the height of first tower, the ball will hit the earth at a distance of
A.
50 m
B.
100 m
C.
200 m
D.
$50\sqrt{2}$ m
Advance Level Q71 Errorless Horizontal Range MCQ
A shell is fired vertically upwards with a velocity $v_{1}$ from the deck of a ship travelling at a speed of $v_{2}$ . A person on the shore observes the motion of the shell as parabola whose horizontal range is given by
A.
$\frac{2v_{1}^{2}v_{2}}{g}$
B.
$\frac{2v_{1}v_{2}^{2}}{g}$
C.
$\frac{2v_{1}v_{2}}{g}$
D.
$\frac{2v_{1}^{2}v^{2}}{g}$
Advance Level Q72 Errorless Horizontal Range MCQ
A boy standing on a long rail road car throws a ball straight upward. The car is moving on the horizontal road with an acceleration of $1m / s^2$ and the projection velocity in the vertical direction is $9.8m / s$ . How far behind the boy will the ball fall on the car
A.
$1m$
B.
$2m$
C.
$4m$
D.
$0.5m$
Advance Level Q73 Errorless Horizontal Range MCQ
Two projectiles A and B thrown with velocities v and $\frac{v}{2}$ have the same range. If B is thrown at an angle of $15^{\circ}$ to the horizontal, A must have been thrown at an angle
A.
$\sin^{-1}\left(\frac{1}{16}\right)$
B.
$\sin^{-1}\left(\frac{1}{4}\right)$
C.
$2\sin^{-1}\left(\frac{1}{4}\right)$
D.
$\frac{1}{2}\sin^{-1}\left(\frac{1}{8}\right)$
Advance Level Q74 Errorless Horizontal Range MCQ
A body is projected with a speed u in such a direction that the maximum height obtained is equal to its horizontal range. The horizontal range is
A.
$\frac{8u^{2}}{17g}$
B.
$\frac{5u^{2}}{17g}$
C.
$\frac{6u^{2}}{13g}$
D.
$\frac{u^{2}}{2g}$
Advance Level Q75 Errorless Horizontal Range MCQ
A body of mass m thrown horizontally with velocity v, from the top of tower of height h touches the level ground at a distance of 250 m from the foot of the tower. A body of mass 2m, thrown horizontally with a velocity v/2, from the top of tower of height 4 h will touch the level ground at a distance from the foot of tower
A.
250 m
B.
500 m
C.
125 m
D.
$250 \sqrt{2}$ m