Practice Paper 3 (Mechanics) (Edexcel A Level Maths: Pure)

Two stones are slid across a large icy pond. The first stone is released from rest at the origin with constant acceleration The second stone is released from rest from the position with coordinates with constant acceleration  .

Show that the two stones collide after 10 seconds.

A stone is thrown from the edge of a deep cave such that it will fall into the cave and has velocity

at time t seconds after it is thrown. 

Find the position of the stone at the time it is about to fall into the cave (rather than being in the air above the cave).

Find the maximum height above the cave the stone reaches.

The deepest known cave in the world has a depth of 2212 m. (The Veryovkina Cave in Georgia.) The model above suggests the stone would take around  to reach this depth. Consider the average speed and the acceleration of the stone to highlight a problem with this model.

In the following diagram  is a ladder of length 10 m and mass 34 kg.  End  of the ladder is resting against a smooth vertical wall, while end  rests on rough horizontal ground so that the ladder makes an angle of  with the ground as shown below:

A housepainter with a mass of 75 kg has decided to climb up the ladder without taking any additional precautions to prevent the bottom of the ladder from slipping.  The ladder may be modelled as a uniform rod lying in a vertical plane perpendicular to the wall, and the housepainter may be modelled as a particle.  The coefficient of friction between the ground and the ladder is 0.4.

Luckily, the housepainter’s partner convinces him not to climb up the ladder without providing some additional support at the bottom to prevent slipping.  If the housepainter had continued with his original plan, however, how far above the ground would he have been when the ladder began to slip?

A golfer strikes a ball from ground level with velocity

Find the distance the golf ball will travel before first hitting the ground.

Show that by reducing the angle of the strike above the horizontal by  the golfer can achieve approximately 7 m more distance before the ball lands.

Give a reason why the golfer may not want to achieve a longer distance with their shot.

To crash test cars, a computer‑controlled car is accelerated along a horizontal track and crashed into a wall. The maximum length of track available is 1.1 km long.

During a crash test, of track is required to increase a car’s speed from rest to . From this point onwards a car is accelerated at a constant rate. This is set to but can be varied up or down by 30% prior to a test being carried out.

Find the acceleration of a car during the first 20 m of a crash test.

Determine if it is possible to crash test a car at a speed of .

A crash test is unreliable if it takes under 10 seconds.
Find the lowest speed, in kilometres per hour, a car can be reliably crash tested at.

A snooker ball is struck such that it travels in a straight line up and down a snooker table. The graph below shows the velocity of the ball, , at time  after being struck.