The height y and the distance x along the vertical plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y=(8t-5t^2)$ meter and x = 6t meter, where t is in second. The velocity with which the projectile is projected is 

(1) 8 m/sec

(2) 6 m/sec

(3) 10 m/sec

(4) Not obtainable from the data

Referring to above question, the angle with the horizontal at which the projectile was projected is 

(1) tan^–1(3/4)

(2) tan^–1(4/3)

(3) sin^–1(3/4))

(4) Not obtainable from the given data

Referring to the above two questions, the acceleration due to gravity is given by 

(1) 10 m/sec²

(2) 5 m/sec²

(3) 20 m/sec²

(4) 2.5 m/sec²

The range of a particle when launched at an angle of 15° with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of 45° to the horizontal 

(1) 1.5 km

(2) 3.0 km

(3) 6.0 km

(4) 0.75 km

Galileo writes that for angles of projection of a projectile at angles $(45+\theta )$ and $(45-\theta )$, the horizontal ranges described by the projectile are in the ratio of (if $\theta \le 45$) 

1. 2 : 1

2. 1 : 2

3. 1 : 1

4. 2 : 3

A projectile thrown with a speed v at an angle θ has a range R on the surface of earth. For same v and θ, its range on the surface of moon will be (acceleration due to gravity on moon=$\frac{g}{6}$):

(1) R/6

(2) 6 R

(3) R/36

(4) 36 R

A ball is projected with kinetic energy E at an angle of 45° to the horizontal. At the highest point during its flight, its kinetic energy will be 

(1) Zero

(2) $\frac{E}{2}$

(3) $\frac{E}{\sqrt{2}}$

(4) E

At the top of the trajectory of a projectile, the magnitude of the acceleration is

(1) Maximum

(2) Minimum

(3) Zero

(4) g

A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is 

(1) ${25}^o{8}^{\text{'}}$

(2) ${33}^o{7}^{\text{'}}$

(3) ${42}^o{8}^{\text{'}}$

(4) ${53}^o{8}^{\text{'}}$

Two bodies are projected with the same velocity. If one is projected at an angle of 30° and the other at an angle of 60° to the horizontal, the ratio of the maximum heights reached is 

(1) 3 : 1

(2) 1 : 3

(3) 1 : 2

(4) 2 : 1