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 \(𝑦 = ( 8 𝑡 − 5t^ 2 )\) meter and \(x = 6t\) meter, where \(t\) is in seconds. The velocity with which the projectile is projected is:

1. \(8\ \text{m/s}\)

2. \(6\ \text{m/s}\)

3. \(10\ \text{m/s}\)

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 \(1.5\ \text{km}\). What is the range of the projectile when launched at an angle of \(45^°\) to the horizontal:

1. \(1.5\ \text{km}\)

2. \(3.0\ \text{km}\)

3. \(6.0\ \text{km}\)

4. \(0.75\ \text{km}\)

Galileo writes that for angles of projection of a projectile at angles \(( 45 + 𝜃 )\) and \(( 45 − 𝜃 )\), the horizontal ranges described by the projectile are in the ratio of \((\text{if}\ 𝜃 ≤ 45 ) \):

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 the Earth. For same \(v\) and \(θ\), its range on the surface of the Moon will be \(\left(\text{acceleration due to gravity on moon}=\dfrac g6\right)\):

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. \(\dfrac E2\)

3. \(\dfrac E{\sqrt2}\)

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. \(25^\circ 8 '\)

2. \(33^\circ 7 '\)

3. \(42^\circ 8 '\)

4. \(53^\circ 8 '\)

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.  \( 2 : 1\)