Gravitation test questions

1

An arrow is fired with a velocity of \(27m {s^{ - 1}}\) at \(25^\circ\) above the horizontal. It lands on level ground.

An arrow travelling at a velocity of 27 metres per second at an angle of 25 degrees above the horizontal.

Calculate the vertical component of initial velocity.

2

An arrow is fired with a velocity of \(27m{s^{ - 1}}\) at \(25^\circ\) above the horizontal. It lands on level ground.

An arrow travelling at a velocity of 27 metres per second at an angle of 25 degrees above the horizontal.

Calculate the horizontal component of initial velocity.

3

An arrow is fired with a velocity of \(27m{s^{ - 1}}\) at \(25^\circ\) above the horizontal. It lands on level ground.

An arrow travelling at a velocity of 27 metres per second at an angle of 25 degrees above the horizontal.

Calculate the total time of flight.

4

An arrow is fired with a velocity of \(27m{s^{ - 1}}\) at \(25^\circ\) above the horizontal. It lands on level ground.

An arrow travelling at a velocity of 27 metres per second at an angle of 25 degrees above the horizontal.

Calculate the maximum height reached.

5

An arrow is fired with a velocity of \(27m{s^{ - 1}}\) at \(25^\circ\) above the horizontal. It lands on level ground.

An arrow travelling at a velocity of 27 metres per second at an angle of 25 degrees above the horizontal.

Calculate the total horizontal distance travelled by the arrow.

6

A projectile is fired at an angle \(\theta\) to the horizontal.

The horizontal and vertical components of velocity of the projectile at the instant of firing are shown in the diagram.

Vector diagram for projectile fired at angle theta to the horizontal. Vertical component of velocity is 50 metres per second. Horizontal component is 30 metres per second.

What will the horizontal and vertical components of the velocity be after one second? The effects of air resistance may be neglected.

7

Calculate the force acting between the Earth and the Moon using this data:

Mass of the Earth is \(5.98 \times {10^{24}}kg\)

Mass of the Moon is \(7.35 \times {10^{22}}kg\)

Radius of Earth \(6300km\,(6.3 \times {10^6}m)\)

Radius of the Moon \(1700km\,(1.7 \times {10^6}m)\)

Distance from surface of Earth to surface of the Moon \(384\,000km\,(3.84 \times {10^8}m)\) (an average – it varies!)

Gravitational constant \(6.67 \times {10^{ - 11}}{m^3}k{g^{ - 1}}{s^{ - 2}}\)