For a particle projected on a horizontal surface, the ratio of range to maximum height is:
( is the angle of projection with respect to horizontal):
(1) 4cot
(2) 4tan
(3) 0.25cot
(4) 0.25sin
Two projectiles, one fired from the surface of the earth with speed 5 m/s and the other fired from the surface of a planet with initial speed 3 m/s with the same angle of the projection, trace identical trajectories. Neglecting friction effect, the value of acceleration due to gravity on the planet is:
(1) 5.9
(2) 3.6
(3) 16.3
(4) 8.5
A projectile is projected from origin of a co-ordinate system with initial velocity of m/s considering y-axis along vertical. The equation of its trajectory is (take g = 10 )
(1) 6y = 4x - 5
(2) 5y = 6x - 4
(3) 4y = 6x - 5
(4) 6y = 5x - 4
During the downward motion of an oblique projectile from the top point of its trajectory, the radius of curvature of its trajectory will:
(1) Remain constant
(2) Increase
(3) Decrease
(4) May increase or decrease
A particle is thrown obliquely at \(t=0\). The particle has the same K.E. at \(t=5\) seconds and at \(t=9\) seconds. The particle attains maximum altitude at:
1. \(t=6\) s
2. \(t=7\) s
3. \(t=8\) s
4. \(t=14\) s
A particle of mass m is thrown at t=0 with kinetic energy at an angle 30° with the horizontal from the top of a tower of height 80 m. The particle again has kinetic energy after time . The is equal to:
(1)
(2)
(3)
(4)
1. | parallel to the position vector. |
2. | at \(60^{\circ}\) with position vector. |
3. | parallel to the acceleration vector. |
4. | perpendicular to the position vector. |
Which of the following angles of projections will provide a maximum range to a projectile when projected with the same speed in all cases?
(1) 37°
(2) 54°
(3) 42°
(4) 49°
If a body is projected from the surface of the earth for maximum range R, then the maximum height attained by the body is:
(1) R
(2)
(3) 4R
(4)
A projectile is projected from the ground with the velocity \(v_{0}\) at an angle \(\theta\) with the horizontal. What is the vertical component of the velocity of the projectile when its vertical displacement is equal to half of the maximum height attained?
1. \(\sqrt{3} v_{0}\cos\theta\)
2. \(\frac{v_{0}}{\sqrt{2}} \sin\theta\)
3. \(\frac{v_{0}}{\sqrt{2}} \cos \theta\)
4. \(\sqrt{5} v_{0}\)