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. \(\sqrt{5} v_{0}\)
A projectile is projected with a speed of 60 m/s at an angle of 60° from the horizontal. After some time projectile is moving at an angle of 30° with horizontal, what is the value of at this instant? (Given g = 10 )
(1) 1
(2)
(3)
(4) 5
A particle is rotating with increasing speed on a circular track. The angle between its radius vector and acceleration is , then:
(1) 0° < < 90°
(2) 45° < < 90°
(3) 90° < < 180°
(4) = 90°
A particle starts moving on a circular path from rest, such that its tangential acceleration varies with time as \(a_t=kt\). Distance traveled by particle on the circular path in time \(t\) is:
1. \(
\frac{kt^3}{3}
\)
2. \(\frac{kt^2}{6}
\)
3. \(\frac{kt^3}{6}
\)
4. \(\frac{k t^2}{2}\)
A projectile thrown from the ground has horizontal range R. If velocity at the highest point is doubled somehow, the new range will be:
(1) 3 R
(2) 1.5 R
(3) R
(4) 2 R