An object is thrown along a direction inclined at an angle of 45° with the horizontal direction. The horizontal range of the particle is equal to 

(1) Vertical height

(2) Twice the vertical height

(3) Thrice the vertical height

(4) Four times the vertical height

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