A golfer strikes a ball so that it leaves horizontal ground with a velocity of 6.0 ms⁻¹ at an angle θ to the horizontal, as illustrated in Fig. 1.1. [Figure 1.1] The magnitude of the initial vertical component v_y of the velocity is 4.8 ms⁻¹. Assume that air resistance is negligible.

1. (a)Show that the magnitude of the initial horizontal component v_x of the velocity is 3.6 ms⁻¹.[1]
2. (b)(i)On Fig. 1.2, sketch separate lines to show the variation with time t, until the ball returns to the ground, of the vertical component v_y of the velocity (label this line Y),[2]
3. (b)(ii)the horizontal component v_x of the velocity (label this line X).[2]
4. (c)Calculate the maximum height reached by the ball. maximum height = ..................................................... m[2]
5. (d)For the movement of the ball from the ground to its maximum height, determine the ratio kinetic energy at maximum height -------------------------------------------------------------- change in gravitational potential energy ratio = ....................................................................[4]
6. (e)In practice, significant air resistance acts on the ball. Explain why the actual time taken for the ball to reach maximum height is less than the time calculated when air resistance is assumed to be negligible.[1]

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