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Kinematics-1D

700 Questions Start Allen Test
All Exams Allen Objective Errorless
Q451 Allen GROUND TO GROUND PROJECTION MCQ
The range of a projectile when fired at $60^{\circ}$ to the horizontal is 0.5 km. What will be its range when fired at $45^{\circ}$ with the same speed?
A.
0.5 km
B.
$\frac{1.0}{\sqrt{3}}$ km
C.
1.5 km
D.
2.0 km
Q452 Allen GROUND TO GROUND PROJECTION MCQ
The speed of a projectile at its maximum height is $\frac{1}{2}$ times of its initial speed 'u' of projection. Its range on the horizontal plane is:
A.
$\frac{\sqrt{3}u^2}{2g}$
B.
$\frac{u^2}{2g}$
C.
$\frac{3u^2}{2g}$
D.
$\frac{3u^2}{g}$
Q453 Allen GROUND TO GROUND PROJECTION MCQ
A bullet is fired from a cannon with velocity 500 m/s. If the angle of projection is $15^{\circ}$ and $g = 10m/s^{2}$ . Then the range is :-
A.
$25 \times 10^{3}$ m
B.
$12.5 \times 10^{3}$ m
C.
$50 \times 10^{2}$ m
D.
$25 \times 10^{2}$ m
Q454 Allen GROUND TO GROUND PROJECTION MCQ
For a given angle of projection if the initial velocity is tripled the range of the projectile becomes :-
A.
9 times
B.
one-fourth
C.
two times
D.
four times
Q455 Allen GROUND TO GROUND PROJECTION MCQ
A ball is thrown at an angle $\theta$ to the vertical and the range is maximum. The value of $\tan\theta$ is:
A.
1
B.
$\sqrt{3}$
C.
$\frac{1}{\sqrt{3}}$
D.
2
Q456 Allen GROUND TO GROUND PROJECTION MCQ
The maximum horizontal range of a gun is 25 km. If g = 10 m/s $^{2}$ , the muzzle velocity of the shell must be:-
A.
1600 m/s
B.
500 m/s
C.
200 $\sqrt{2}$ m/s
D.
160 $\sqrt{10}$ m/s
Q457 Allen GROUND TO GROUND PROJECTION MCQ
A grasshopper can jump maximum distance 1.6 m. It spends negligible time on the ground. How far can it go in 10 seconds:-
A.
$5\sqrt{2}\mathrm{m}$
B.
$10\sqrt{2}\mathrm{m}$
C.
$20\sqrt{2}\mathrm{m}$
D.
$40\sqrt{2}\mathrm{m}$
Q458 Allen GROUND TO GROUND PROJECTION MCQ
Three projectiles A, B and C are thrown from the same point in the same plane. Their trajectories are shown in the figure. Which of the following statement is incorrect?
A.
The time of flight is the same for all the three
B.
The launch speed is same for all the three
C.
The horizontal velocity component is largest for particle C
D.
The maximum height is same for all the three
Q459 Allen GROUND TO GROUND PROJECTION MCQ
A projectile is thrown with an initial velocity of $\vec{v} = a\hat{i} + b\hat{j}$ . If range of the projectile is four times the maximum height attained by it then:
A.
$a = 2b$
B.
$b = a$
C.
$b = 2a$
D.
$b = 4a$
Q460 Allen GROUND TO GROUND PROJECTION MCQ
Two projectiles are fired from the same point with the same speeds at angles of projection $60^{\circ}$ and $30^{\circ}$ respectively. Which one of the following is true?
A.
Their horizontal ranges will be the same
B.
Their maximum heights will be the same
C.
Their landing velocities will be the same
D.
Their times of flight will be the same
Q461 Allen GROUND TO GROUND PROJECTION MCQ
Three particles A, B and C are projected from the same point with the same initial speeds making angles $30^{\circ}$ , $45^{\circ}$ and $60^{\circ}$ respectively with the horizontal. Which of the following statements are correct?
A.
A, B and C have unequal ranges
B.
Ranges of A and C are equal and less than that of B
C.
Ranges of A and C are equal and greater than that of B
D.
A, B and C have equal ranges
Q462 Allen GROUND TO GROUND PROJECTION MCQ
A number of bullets are fired in all possible directions with the same initial velocity u. The maximum area of ground covered by bullets is:-
A.
$\pi\left(\frac{2u^{2}}{g}\right)^{2}$
B.
$3\pi\left(\frac{u}{g}\right)^{2}$
C.
$5\pi\left(\frac{u}{2g}\right)^{2}$
D.
$\pi\left(\frac{u^{2}}{g}\right)^{2}$
Q463 Allen GROUND TO GROUND PROJECTION MCQ
Four bodies P, Q, R and S are projected with equal speed having angles of projection $15^{\circ}$ , $30^{\circ}$ , $45^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The body having shortest range is:
A.
P
B.
Q
C.
R
D.
S
Q464 Allen GROUND TO GROUND PROJECTION MCQ
A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance up to which the boy can throw the same stone will be :
A.
$20\sqrt{2}$ m
B.
10 m
C.
$10\sqrt{2}$ m
D.
20 m
Q465 Allen GROUND TO GROUND PROJECTION MCQ
A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground can the cricketer throw the same ball :-
A.
200m
B.
400m
C.
100m
D.
50m
Q466 Allen GROUND TO GROUND PROJECTION MCQ
The cannon was set by mistake at $30^{\circ}$ instead of $20^{\circ}$ with the horizontal and was fired to hit the enemy target. The cannon-shell will now fall at :
A.
The enemy target
B.
Before the enemy target
C.
Beyond the enemy target
D.
May fall at any place
Q467 Allen GROUND TO GROUND PROJECTION MCQ
Two similar cannon simultaneously fires two identical cannon balls at target 1 and 2 as shown in the figure. If the cannon balls have identical initial speeds, which of the following statements is true?
A.
Target 2 is hit before target 1
B.
Target 1 is hit before target 2
C.
Both are hit at the same time
D.
information is insufficient
Q468 Allen GROUND TO GROUND PROJECTION MCQ
If R is the horizontal range of a particle projected at an angle $53^{\circ}$ from horizontal, then the greatest height attained by it is:
A.
$\frac{R}{3}$
B.
2R
C.
$\frac{R}{2}$
D.
$\frac{R}{4}$
Q469 Allen GROUND TO GROUND PROJECTION MCQ
A projectile can have the same range R for two angles of projection. If $h_{1}$ and $h_{2}$ be the maximum height in the two cases, then:
A.
$h_{1}h_{2} \propto R^{2}$
B.
$h_{1}h_{2} \propto R$
C.
$h_{1}h_{2} \propto \frac{1}{R}$
D.
$h_{1}h_{2} \propto \frac{1}{R^{2}}$
Q470 Allen GROUND TO GROUND PROJECTION MCQ
A body is thrown with some velocity from the ground. Maximum height attained when it is thrown at $37^{\circ}$ to the horizontal is 90 m. What is the height attained when it is thrown at $53^{\circ}$ to the horizontal?
A.
90 m
B.
45 m
C.
120 m
D.
160 m
Q471 Allen GROUND TO GROUND PROJECTION MCQ
Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\frac{\pi}{6}$ and its maximum height is $y_{1}$ , then the maximum height of the other will be:
A.
$3y_{1}$
B.
$2y_{1}$
C.
$\frac{y_{1}}{2}$
D.
$\frac{y_{1}}{3}$
Q472 Allen GROUND TO GROUND PROJECTION MCQ
A ball is thrown at different angles with the same speed u and from the same point; it has the same range in both the cases. If $y_{1}$ and $y_{2}$ be the heights attained in the two cases, then $y_{1} + y_{2} = \ldots$ :
A.
$\frac{u^{2}}{g}$
B.
$\frac{2u^{2}}{g}$
C.
$\frac{u^{2}}{2g}$
D.
$\frac{u^{2}}{4g}$
Q473 Allen GROUND TO GROUND PROJECTION MCQ
A body is projected at such an angle that the horizontal range is four times the greatest height. The angle of projection is:-
A.
$25^{\circ}$
B.
$33^{\circ}$
C.
$45^{\circ}$
D.
$53^{\circ}$
Q474 Allen GROUND TO GROUND PROJECTION MCQ
The horizontal range of a projectile is $4\sqrt{3}$ times of its maximum height. Its angle of projection from horizontal will be:
A.
$45^{\circ}$
B.
$60^{\circ}$
C.
$90^{\circ}$
D.
$30^{\circ}$
Q475 Allen GROUND TO GROUND PROJECTION MCQ
A projectile have range double as compare to its maximum height attained. The angle of projection from horizontal is-
A.
$\tan^{-1}(2)$
B.
$\tan^{-1}(4)$
C.
$\tan^{-1}(3)$
D.
$\tan^{-1}(5)$