2.1 Motion

An experimenter throws a small object upwards. The graph shows the variation of velocity v with time t of the object. 

The experimenter states that the velocity-time graph shows the object travels the same distance upwards and it does downwards. 

Examination questions on projectile motion often involves objects moving vertically through the atmosphere. 

The object shown moves vertically downwards through the atmosphere.

Often, a simplifying condition is assumed so that, in these cases, only a single force acts on objects as they move through the atmosphere. 

Terminal velocity is only attained if both forces act on the object. 

An experiment designed to measure the acceleration due to gravity is set up as shown. 

The two-way switch is connected at A to an electromagnet and at B to a trap door, via an electric stop-clock. The stop-clock starts the instant the switch moves from A to B, and stops when the trap door is opened by a falling steel ball, which breaks the circuit. 

The distance travelled s acts as the independent variable in this experiment. 

Use the equation of motion for the steel ball, 

to help answer the following questions:

(ii)

Show that the equation of motion for the steel ball becomes:

[1]

The time taken t for the steel ball to descend different distances s is measured. The graph shows the variation of the distance s with the square of time, t². 

(i)

Explain why the equation of motion can be written as: 

[1]

Projectiles follow parabolic trajectories. One such trajectory is shown for a projectile fired from a bazooka. 

The projectile lands on its target with a final velocity v that can be represented as shown. 

The initial horizontal velocity given to the projectile is 3.5 m s^–1. Air resistance can be ignored. 

The final vertical velocity of the projectile is 3.8 m s^–1. 

The horizontal distance between the bazooka and the target is 27 m.