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Kinematics-1D

346 Questions Start Allen Test
All Exams Allen Objective Errorless
Q226 Allen 6. 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.
$\tan^{-1}\left(\frac{8}{5}\right)$
Q227 Allen 6. 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
Q228 Allen 6. 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.
$\frac{1}{2}\sin^{-1}\left(\frac{Rg}{v^{2}}\right)$
Q229 Allen 6. 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.
$\frac{1}{4}\sin^{-1}\left(\frac{1}{8}\right)$
Q230 Allen 6. 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
Q231 Allen 6. 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
Q232 Allen 6. 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°
Q233 Allen 6. 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
Q234 Allen 6. 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.
$90^{\circ}$
Q235 Allen 6. 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
Q236 Allen 6. 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
Q237 Allen 6. 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
Q238 Allen 6. 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 $\theta$
Q239 Allen 6. 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
Q240 Allen 7. 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
Q241 Allen 7. PROJECTION FROM A HEIGHT MCQ
An aeroplane moving horizontally with a speed of 90 km/h drops a food packet while flying at a height of 490 m. The horizontal range of the packet is:
A.
180 m
B.
250 m
C.
500 m
D.
670 m
Q242 Allen 7. PROJECTION FROM A HEIGHT MCQ
A stuntman plans to run along a roof top and then horizontally off it to land on the roof of next building. The roof of the next building is 19.6 metres below the first one and 6.2 metres away from it. What should be his minimum roof top speed in m/s, so that he can successfully make the jump?
A.
3.1
B.
4.0
C.
4.9
D.
6.2
Q243 Allen 7. PROJECTION FROM A HEIGHT MCQ
Two stones are projected horizontally from the same height with speeds 100 m/s and 40 m/s. The ratio of their horizontal range is
A.
1:1
B.
5:2
C.
2:5
D.
3:4
Q244 Allen 7. PROJECTION FROM A HEIGHT MCQ
A body is thrown horizontally with a velocity 20 m/s from the top of a tower of height 20 m. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is :-
A.
20 m
B.
10 m
C.
40 m
D.
30 m
Q245 Allen 7. PROJECTION FROM A HEIGHT MCQ
A bomber is flying horizontally with a constant speed of 150 m/s at a height of 19.6 m. The pilot has to drop a bomb at the enemy target. At what horizontal distance from the target should he release the bomb?
A.
0 m
B.
300 m
C.
600 m
D.
1000 m
Q246 Allen 7. PROJECTION FROM A HEIGHT MCQ
A boy wants to jump from building A to building B. Height of building A is 25 m and that of building B is 5m. Distance between buildings is 8m. Assume that the boy jumps horizontally, then calculate minimum velocity with which he has to jump to land safely on building B.
A.
$6\mathrm{m / s}$
B.
$8\mathrm{m / s}$
C.
$4\mathrm{m / s}$
D.
$2\mathrm{m / s}$
Q247 Allen 7. PROJECTION FROM A HEIGHT MCQ
A boy wants to jump from building A to building B. Height of building A is 39.2 m and building B is 19.6m. Distance between buildings is 20 m. Assuming boy jumps horizontally, then calculate minimum velocity with which boy has to jump to land safely on building B :-
A.
$10\mathrm{m / s}$
B.
$20\mathrm{m / s}$
C.
$9.8\mathrm{m / s}$
D.
$19.6\mathrm{m / s}$
Q248 Allen 7. PROJECTION FROM A HEIGHT MCQ
Two buildings are separated by 30 m. By what speed a ball is projected horizontally from a window at height 150 m in one building so as to enter in the window at height 27.5 m in the other building.
A.
2 m/s
B.
6 m/s
C.
4 m/s
D.
8 m/s
Q249 Allen 7. PROJECTION FROM A HEIGHT MCQ
Two bodies of masses 100 kg and 50 kg are projected horizontally from same height with speeds 40 m/s and 20 m/s, simultaneously. The ratio of time taken by both the bodies to reach the ground is:-
A.
1:1
B.
1:2
C.
2:1
D.
1:4
Q250 Allen 7. PROJECTION FROM A HEIGHT MCQ
A ball is thrown horizontally from a height of 90 m with a speed of 4.5 m/s then find the time when it is at the height of 45 m from the ground:
A.
$3\sqrt{2}$ sec
B.
10 sec
C.
9 sec
D.
3 sec