A ball is projected vertically upwards with an initial speed of 10 m s−1 at a height of 2.5m above the ground. In part (a) ignore all frictional forces.
(a) (i) Draw a force diagram for the ball while it is in motion. [1]
(ii) Define appropriate coordinate axes and an origin, and state the
initial velocity and initial displacement in terms of the unit
vectors and origin that you have chosen. [2]
(iii) Determine, in terms of the magnitude of the acceleration due to
gravity, g, the maximum height that the ball reaches above the
point of projection, and the time taken to reach this position. [3]
(iv) Determine the speed at which the ball hits the ground, correct to two decimal places, taking the value of g to be 9.81m s−2. [2]
In the remainder of the question revise this model by taking air resistance
into account.
Model the ball as a sphere of diameter D and mass m, and
assume that the quadratic model of air resistance applies.