Kinematics (HL IB Physics)

A ball is projected horizontally at 27 m s^–1 from a vertical cliff. It travels a horizontal distance of 40 m before hitting the ground.

Assume that air resistance is negligible.

Calculate the vertical velocity of the ball just before it hits the ground.

Calculate the height of the cliff.

Sketch the graphs to show how the horizontal and vertical components of the velocity of the ball,  and  change with time t just before the ball hits the ground.

Label any appropriate values on the axes.

Calculate the resultant velocity of the ball just before it hits the ground.

Naomi stands on the edge of a vertical cliff and throws a stone vertically upwards.

The stone leaves her hand with a speed of 20 m s^–1 at the instant her hand is 73 m above the surface of the sea. Air resistance is negligible.

Calculate the maximum height reached by the stone as measured from the point it was thrown.

Determine the time taken for the stone to pass by the point from which it was released.

Calculate the time taken for the stone to land in the sea after leaving Naomi’s hand.

Sketch the graph to show how the displacement s of the stone changes with time t from when it is thrown in the air to when it touches the surface of the sea.

 

The graph shows how the velocity v of a particle varies with time t.

At time t = 0 the instantaneous velocity of the particle is 0.

Calculate the instantaneous acceleration of the particle at time t = 6 s.

The velocity of the particle, as shown on the graph on part (a), is its vertical velocity. At t = 5 s, its horizontal velocity is 2.5 m s^–1.

Calculate the angle of the particle from the horizontal at t = 5 s.

A different particle falls under gravity for 0.7 m from rest. Assume that air resistance is negligible.

Calculate:

A third particle now falls under the effect of both gravity and air resistance.

After falling for some time, its resultant force becomes zero for the rest of its motion. It reaches the same final velocity in the same time as the second particle, where air resistance was not present.

Sketch the motion of this third particle on the graph in part (a).

Describe how the fluid resistance on an object in free fall means it reaches a terminal velocity.

A bird drops a spherical graphite rock of density 2230 kg m^–3 and radius 3 cm vertically down a water well. After it hits the water surface, it rapidly reaches a terminal speed as it falls through the well.

Calculate the magnitude of the fluid resistance from the water on the rock whilst it travels at terminal speed.

The bird drops the rock 14 m above the water’s surface.  is the time when the rock hits the water surface and  is when the rock is at rest at the bottom of the well, which is 70 m deep.

Determine the value of  .

Calculate the speed at which the rock hits the water.

Two identical balls are dropped from rest from the same height. One of the balls is dropped 1.50 s after the other.

Calculate the distance that separates the two balls 3.00 s after the second ball is dropped.

Draw the displacement–time graphs for both balls.

One of the balls is now dropped from the same height again from rest. After 2 seconds, it enters a cylinder of oil where it then no longer accelerates.

Sketch on the displacement–time graph the motion of this ball.

A different ball, that is identical in every way but is much heavier than the first two is now dropped from a certain height. Again, after 2 seconds, it enters a cylinder of oil where it then no longer accelerates.  

Compare and contrast how the displacement–time graph from part (c) would change for this heavier ball. Assume that air resistance is negligible.

A rock is thrown off a cliff at a height of 150 m and lands 90 m away. 

Determine the angle at which the rock makes impact with the ground. 

The rock is loaded into a catapult and is launched at 40° elevation from the ground toward a castle wall, with a speed of 27 m s^–1. The castle wall is 50 m away and is 12 m high. 

Determine whether the rock makes it over the wall. 

Prove that the maximum range of any projectile that starts and ends at ground level is achieved when launched at an angle of elevation of 45°. 

You may wish to use the double angle formula:

A truck driver's initial speed is 4.0 m s^–1 when they begin to accelerate at 6.0 m s^–2. After 3.0 seconds, they decelerate at 5.0 m s^–2 to stop at a set of traffic lights. 

Calculate the distance between the traffic lights and the point where the truck began to accelerate. 

Draw the velocity-time graph on the axes provided for the motion of the truck in part (a). 

Sketch the displacement-time and acceleration-time graphs for the truck on the pair of axes provided. Label each axes appropriately. 

An object is released near the surface of the Moon at time t = 0. The graph shows the variation of displacement s with time t of the object from the point of release. 

Use the graph to determine a value for the acceleration of free fall close to the surface of the Moon.

Use the graph to estimate the instantaneous velocity of the object at t = 1.5 s.

A projectile is launched from sea level with an initial velocity v at an angle of θ above the ground.

Assume that air resistance is negligible. 

The launch location and point of impact of the ball in relation to the ground are shown in the diagram.

On the diagram, sketch the trajectory of the ball when: