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Kinematics-1D

346 Questions Start Allen Test
All Exams Allen Objective Errorless
Q176 Allen 6. GROUND TO GROUND PROJECTION MCQ
A body is thrown with a velocity of 19.6 m/s making an angle of $30^{\circ}$ with the horizontal. It will hit the ground after a time:—
A.
3 s
B.
2 s
C.
1.5 s
D.
1 s
Q177 Allen 6. GROUND TO GROUND PROJECTION MCQ
If a projectile is fired at an angle $\theta$ to the vertical with velocity $u$ , then maximum height attained is given by:
A.
$\frac{u^2 \cos \theta}{2g}$
B.
$\frac{u^2 \sin^2 \theta}{2g}$
C.
$\frac{u^2 \sin^2 \theta}{g}$
D.
$\frac{u^2 \cos^2 \theta}{2g}$
Q178 Allen 6. GROUND TO GROUND PROJECTION MCQ
At the uppermost point of a projectile its velocity and acceleration are at an angle of:-
A.
$180^{\circ}$
B.
$90^{\circ}$
C.
$60^{\circ}$
D.
$45^{\circ}$
Q179 Allen 6. GROUND TO GROUND PROJECTION MCQ
Two projectiles are projected with velocity $v_{A}$ , $v_{B}$ at angles $\theta_{A}$ (from horizontal) and $\theta_{B}$ (from vertical) as shown in the figure below, such that $v_{A} > v_{B}$ but having same horizontal component of velocity. Which of the following can not be correct?
A.
$\mathrm{T_A > T_B}$
B.
$\mathrm{H_A > H_B}$
C.
$\mathrm{R_A > R_B}$
D.
$\mathrm{R_B > R_A}$
Q180 Allen 6. GROUND TO GROUND PROJECTION MCQ
A player throws a ball that reaches to the another player in 4s. If the height of each player is 1.5m, the maximum height attained by the ball from the ground level is:
A.
19.6 m
B.
21.1 m
C.
23.6 m
D.
25.1 m
Q181 Allen 6. GROUND TO GROUND PROJECTION MCQ
A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with speed v. While rising up the magnitude of the velocity after t seconds will be:
A.
$\sqrt{(v\cos\theta)^2 + (v\sin\theta)^2}$
B.
$\sqrt{(v\cos\theta - v\sin\theta)^2 - gt}$
C.
$\sqrt{v^2 + g^2t^2 - (2v\sin\theta)gt}$
D.
$\sqrt{v^2 + g^2t^2 - (2v\cos\theta)gt}$
Q182 Allen 6. GROUND TO GROUND PROJECTION MCQ
A particle is fired with velocity u making $\theta$ angle with the horizontal. What is the magnitude of change in velocity when it returns to the ground.
A.
u cos $\theta$
B.
u
C.
2u sin $\theta$
D.
(u cos $\theta - u$ )
Q183 Allen 6. GROUND TO GROUND PROJECTION MCQ
In the above, the change in speed is:
A.
u cos θ
B.
0
C.
u sin θ
D.
(u cosθ - u)
Q184 Allen 6. GROUND TO GROUND PROJECTION MCQ
The angle which the velocity vector of a projectile, will make with the vertical after time t of its being thrown with a velocity v at an angle $\theta$ to the horizontal, is:
A.
$\theta$
B.
$\tan^{-1}\left(\frac{\theta}{t}\right)$
C.
$\tan^{-1}\left(\frac{v\cos\theta}{v\sin\theta-gt}\right)$
D.
$\tan^{-1}\left(\frac{v\sin\theta-gt}{v\cos\theta}\right)$
Q185 Allen 6. GROUND TO GROUND PROJECTION MCQ
At a height 0.4 m from the ground, the velocity of a projectile in vector form is: $\vec{v}=(6\hat{i}+2\hat{j})$ m/s. The angle of projection from horizontal is $(g=10\mathrm{~m/s^{2}})$:-
A.
$45^{\circ}$
B.
$60^{\circ}$
C.
$30^{\circ}$
D.
$\tan^{-1}(3/4)$
Q186 Allen 6. GROUND TO GROUND PROJECTION MCQ
In case of a projectile fired at an angle $60^{\circ}$ to the horizontal with velocity u, the horizontal range is:
A.
$\frac{u^{2}}{g}$
B.
$\frac{\sqrt{3}u^{2}}{2g}$
C.
$\frac{2u^{2}}{g}$
D.
$\frac{u^{2}}{g^{2}}$
Q187 Allen 6. GROUND TO GROUND PROJECTION MCQ
If the instantaneous velocity of a particle projected as shown in figure is given by $\vec{v}=a\hat{i}+(b-ct)\hat{j}$ 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
Q188 Allen 6. GROUND TO GROUND PROJECTION MCQ
A projectile is thrown from a point in a horizontal plane such that its horizontal and vertical velocity components are 9.8 m/s and 4.9 m/s respectively. Its horizontal range is:
A.
4.9 m
B.
9.8 m
C.
19.6 m
D.
39.2 m
Q189 Allen 6. GROUND TO GROUND PROJECTION MCQ
A projectile is projected with initial velocity $(5\hat{i}+12\hat{j})$ m/s. If g = 10 ms $^{-2}$ , then horizontal range is :
A.
4.8 metre
B.
9.6 metre
C.
19.2 metre
D.
12 metre
Q190 Allen 6. GROUND TO GROUND PROJECTION MCQ
A shell is fired vertically upwards with a velocity $v_{1}$ from the deck of a ship moving with a speed $v_{2}$ . A person on the shore observes the motion of the shell as a parabola. Its 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.
$\frac{2v_{1}^{2}v_{2}^{2}}{g}$
Q191 Allen 6. 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
Q192 Allen 6. 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.
$\frac{3u^2}{g}$
Q193 Allen 6. 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
Q194 Allen 6. 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
Q195 Allen 6. 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
Q196 Allen 6. 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
Q197 Allen 6. 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.
$40\sqrt{2}\mathrm{m}$
Q198 Allen 6. 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
Q199 Allen 6. 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.
$b = 4a$
Q200 Allen 6. 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