Show that the horizontal and vertical displacements, x, y, of a projectile at time t are x

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Show that the horizontal and vertical displacements, x, y, of a projectile at time t are x and y, respectively, where

x = ut and y = vt - gt 2

where u and v are the initial horizontal and vertical velocities and g is the acceleration due to gravity. Show that its trajectory is a parabola, and that it attains a maximum height v2/2g and range 2uv/g.

U18 Horizontal velocity Time V- V 0 Vertical velocity Average Time O (a) (b) Figure 2.45 (a) Velocity-time

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