In the motion of a projectile under gravity, its:

1. Total energy is conserved

2. Momentum is conserved

3. Energy and momentum are both conserved

4. None is conserved

The range of a projectile for a given initial velocity is maximum when the angle of projection is \(45^°\). The range will be minimum if the angle of projection is:

1. \(90^°\)

2. \(180^°\)

3. \(60^°\)

4. \(75^°\)

A ball is thrown upwards and it returns to the ground describing a parabolic path. Which of the following remains constant?

(1) Kinetic energy of the ball

(2) Speed of the ball

(3) Horizontal component of velocity

(4) Vertical component of velocity

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 \(𝑦 = ( 8 𝑡 − 5t^ 2 )\) 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. \(2 : 3\)