An astronaut on the Moon, where there is no air resistance, throws a ball. The ball’s initial velocity has a vertical component of 8.00 m s-1 and a horizontal component of 4.00 m s-1, as shown.

Question 19

An astronaut on the Moon, where there is no air resistance, throws a ball. The ball’s initial velocity has a vertical component of 8.00 m s^-1 and a horizontal component of 4.00 m s^-1, as shown.

The acceleration of free fall on the Moon is 1.62 m s^-2.

What will be the speed of the ball 9.00 s after being thrown?

A 6.6 m s^-1                        B 7.7 m s^-1                        C 10.6 m s^-1                     D 14.6 m s^-1

Reference: Past Exam Paper – November 2016 Paper 11 & 13 Q7

Solution:

Answer: B.

The weight of the ball would affect the vertical component of the velocity as it acts downwards, towards the surface of the Moon.

The absence of air resistance indicates that the horizontal component of velocity is NOT affected during the motion. This component remains constant even after 9 s.

Consider the vertical component.

Take the upward direction to be positive.

Initial velocity, u = + 8.00 m s^-1

Acceleration, a = – 1.62 m s^-2 (as it acts downwards)

Time t = 9.00 s

Final velocity = v

v = u + at = 8 + (–1.62 × 9)

v = - 6.58 m s^-1 (it is downwards)

So, after 9.00 s,

Horizontal component = 4.00 m s^-1

Vertical component = (-) 6.58 m s^-1

The speed v can be found by applying Pythagoras’ theorem.

v² = 4² + 6.58²

v = 7.7 m s^-1