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Kinematics-1D

700 Questions Start Allen Test
All Exams Allen Objective Errorless
Q476 Allen GROUND TO GROUND PROJECTION MCQ
The speed of a projectile at its maximum height is $\frac{\sqrt{3}}{2}$ times its initial speed. If the range of the projectile is 'P' times the maximum height attained by it, then P equals to -
A.
$\frac{4}{3}$
B.
$2\sqrt{3}$
C.
$4\sqrt{3}$
D.
$\frac{3}{4}$
Q477 Allen GROUND TO GROUND PROJECTION MCQ
A ball is projected to attain the maximum range. If the height attained is H, the range is
A.
H
B.
2H
C.
4H
D.
H/2
Q478 Allen GROUND TO GROUND PROJECTION MCQ
The equation of a projectile is $y = x - \frac{gx^2}{2}$ . The angle of projection is:
A.
30Ā°
B.
60Ā°
C.
45Ā°
D.
none
Q479 Allen GROUND TO GROUND PROJECTION MCQ
The equation of a projectile is $y = 4x - \frac{x^{2}}{4}$ . The horizontal range is:
A.
16 m
B.
8 m
C.
64 m
D.
12.8 m
Q480 Allen GROUND TO GROUND PROJECTION MCQ
A particle is projected at an angle of $45^{\circ}$ from horizontal, 6m away from the foot of a wall, just touches the top of the wall and falls on the ground on the opposite side at a distance 3m from it. The height of wall is:
A.
2m
B.
$\frac{4}{3}$ m
C.
$\frac{8}{3}$ m
D.
$\frac{3}{4}$ m
Q481 Allen GROUND TO GROUND PROJECTION MCQ
A stone is projected from the ground with velocity 50 m/s at an angle of $30^{\circ}$ from horizontal. It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground (g = 10m/sec $^{2}$ )
A.
90.2 m
B.
89.6 m
C.
86.6 m
D.
70.2 m
Q482 Allen GROUND TO GROUND PROJECTION MCQ
A shell fired from the ground is just able to cross the top of a wall 90m away and 45 m high moving horizontally. The direction of projection of the shell from horizontal will be :-
A.
$25^{\circ}$
B.
$30^{\circ}$
C.
$60^{\circ}$
D.
$45^{\circ}$
Q483 Allen GROUND TO GROUND PROJECTION MCQ
An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , then the horizontal component of the velocity of arrow is:
A.
40 m/s
B.
20 m/s
C.
31.25 m/s
D.
12.5 m/s
Q484 Allen GROUND TO GROUND PROJECTION MCQ
An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , the maximum height attained by the arrow is:
A.
25 m
B.
20 m/s
C.
31.25 m
D.
12.5 m
Q485 Allen GROUND TO GROUND PROJECTION MCQ
An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , the vertical component of the projection velocity is:
A.
25 m/s
B.
40 m/s
C.
12.5 m/s
D.
31.25 m/s
Q486 Allen GROUND TO GROUND PROJECTION MCQ
An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , the angle of projection with the horizontal is:
A.
$\tan^{-1}\left(\frac{4}{5}\right)$
B.
$\tan^{-1}\left(\frac{5}{4}\right)$
C.
$\tan^{-1}\left(\frac{5}{8}\right)$
D.
$\tan^{-1}\left(\frac{8}{5}\right)$
Q487 Allen GROUND TO GROUND PROJECTION MCQ
A projectile is thrown into space so as to have the maximum possible horizontal range equal to 200m. Taking the point of projection as the origin, the coordinates of the point where the velocity of the projectile is minimum are:
A.
(200, 100) m
B.
(50, 200) m
C.
(100, 50) m
D.
(50, 100) m
Q488 Allen GROUND TO GROUND PROJECTION MCQ
If the range of a gun which fires a shell with muzzle speed v, is R, then the angle of elevation of the gun is:
A.
$\cos^{-1}\left(\frac{v^{2}}{Rg}\right)$
B.
$\cos^{-1}\left(\frac{Rg}{v^{2}}\right)$
C.
$\frac{1}{2}\sin^{-1}\left(\frac{v^{2}}{Rg}\right)$
D.
$\frac{1}{2}\sin^{-1}\left(\frac{Rg}{v^{2}}\right)$
Q489 Allen GROUND TO GROUND PROJECTION MCQ
Two balls A and B are thrown with speeds u and u/2 respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the angle of projection of ball B is $30^{\circ}$ with the horizontal, then the angle of projection of A is:
A.
$\sin^{-1}\left(\frac{1}{8}\right)$
B.
$\frac{1}{2}\sin^{-1}\left(\frac{\sqrt{3}}{8}\right)$
C.
$\frac{1}{3}\sin^{-1}\left(\frac{1}{8}\right)$
D.
$\frac{1}{4}\sin^{-1}\left(\frac{1}{8}\right)$
Q490 Allen GROUND TO GROUND PROJECTION MCQ
Two balls are projected from the same point on the ground simultaneously. First ball is projected vertically upwards and the second ball at an angle of projection $60^{\circ}$ from the horizontal. Both the balls reach the ground simultaneously. The ratio of their velocities of projection are:
A.
1:2
B.
3:2
C.
$\sqrt{3}$ :2
D.
2:3
Q491 Allen GROUND TO GROUND PROJECTION MCQ
A body is projected at an angle $\theta$ with horizontal, another body is projected with the same speed at an angle $\theta$ with the vertical then the ratio of the maximum height is:
A.
$1:1$
B.
$\tan^2\theta:1$
C.
$1:\cot\theta$
D.
none of these
Q492 Allen GROUND TO GROUND PROJECTION MCQ
A ball is thrown from a point on earth surface with a speed v at an angle of projection Īø from horizontal. From the same point and at the same instant a person starts running with a constant speed $\frac{v}{2}$ to catch the ball. The angle of projection of the ball from horizontal is:
A.
60Ā°
B.
30Ā°
C.
90Ā°
D.
45Ā°
Q493 Allen GROUND TO GROUND PROJECTION MCQ
For a projectile the ratio of maximum height reached to the square of flight time is $(g=10\ m/s^{2})$ :-
A.
5:4
B.
5:2
C.
5:1
D.
10:1
Q494 Allen GROUND TO GROUND PROJECTION MCQ
At what angle to the horizontal should a ball be thrown so that its range R is related to the time of flight T as $R = 5\sqrt{3}T^{2}$ ? Take $g = 10 ms^{-2}$ :
A.
$30^{\circ}$
B.
$45^{\circ}$
C.
$60^{\circ}$
D.
$90^{\circ}$
Q495 Allen GROUND TO GROUND PROJECTION MCQ
A ball whose kinetic energy is E, is thrown at an angle of $60^{\circ}$ to the horizontal. Its kinetic energy at the highest point of its flight will be:-
A.
$\frac{E}{4}$
B.
$\frac{E}{\sqrt{2}}$
C.
$\frac{E}{2}$
D.
zero
Q496 Allen GROUND TO GROUND PROJECTION MCQ
A cricket ball is hit at an angle of $30^{\circ}$ with the vertical with kinetic energy K. The kinetic energy of the ball at the highest point of the path is :-
A.
Zero
B.
K/4
C.
K/2
D.
3K/4
Q497 Allen GROUND TO GROUND PROJECTION MCQ
A ball is projected vertically upwards with a certain speed. Another ball of the same mass is projected at an angle $30^{\circ}$ to the vertical with the same initial speed. The ratio of their potential energies at highest points of their journey, will be
A.
4:3
B.
2:1
C.
3:2
D.
4:1
Q498 Allen GROUND TO GROUND PROJECTION MCQ
A particle is projected with a velocity u making an angle $\theta$ with the horizontal. At any instant, its velocity v is at right angle to its initial velocity u; then v is:
A.
u cos $\theta$
B.
u tan $\theta$
C.
u cot $\theta$
D.
u sec $\theta$
Q499 Allen GROUND TO GROUND PROJECTION MCQ
A force $\vec{\mathrm{F}} = (6\mathrm{t}^2\hat{\mathrm{i}} +4\mathrm{t}\hat{\mathrm{j}})\mathrm{N}$ acts on a particle of mass $1\mathrm{kg}$ . What will be velocity of the particle at $t = 3$ second if at $t = 0$ , the particle was at rest:
A.
$(54\hat{\mathrm{i}} +12\hat{\mathrm{j}})\mathrm{m / s}$
B.
$(54\hat{\mathrm{i}} +18\hat{\mathrm{j}})\mathrm{m / s}$
C.
$(12\hat{\mathrm{i}} +6\hat{\mathrm{j}})\mathrm{m / s}$
D.
none
Q500 Allen PROJECTION FROM A HEIGHT MCQ
A stone is projected horizontally with a speed 10 m/s from a 80 m high building. The distance of the target on the ground from the foot of the building is: $(g = 10 \, \text{m/s}^2)$
A.
80 m
B.
40 m
C.
20 m
D.
10 m