# 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)

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.

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