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2 A particle is projected from the origin with speed V m/s at an angle a to the horizontal. 4 a Assuming that the coordinates of the particle at time t are (Vt cos a, Vt sin a gt²), prove that the horizontal range R of the particle V² sin 2a is X2 - Jum b Hence prove that the path of the particle has equation y = x(1 tan a. R c Suppose that a = 45° and that the particle passes through two points 6 metres apart and 4 metres above the point of projection, as shown in the diagram. Let x, and x2 be the x-coordinates of the two points. i Show that x1 and x2 are the roots of the equation x2 ii Use the identity (x2 – x1) = (x2 + x1)² – 4x2x¡ to find R. Rx + 4R = 0. %3D

2 A particle is projected from the origin with speed V m/s at an angle a to the horizontal. 4 a Assuming that the coordinates of the particle at time t are (Vt cos a, Vt sin a gt²), prove that the horizontal range R of the particle V² sin 2a is X2 - Jum b Hence prove that the path of the particle has equation y = x(1 tan a. R c Suppose that a = 45° and that the particle passes through two points 6 metres apart and 4 metres above the point of projection, as shown in the diagram. Let x, and x2 be the x-coordinates of the two points. i Show that x1 and x2 are the roots of the equation x2 ii Use the identity (x2 – x1) = (x2 + x1)² – 4x2x¡ to find R. Rx + 4R = 0. %3D

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12 A particle is projected from the origin with speed V m/s at an angle a to the yA horizontal. a Assuming that the coordinates of the particle at time t are (Vt cos a, Vt sin a – ¿gt2), prove that the horizontal range R of the particle v² sin 2a is X2 6. b Hence prove that the path of the particle has equation y = x X tan a. R 1 - c Suppose that a = 45° and that the particle passes through two points 6 metres apart and 4 metres above the point of projection, as shown in the diagram. Let x, and x2 be the x-coordinates of the two points. i Show that ii Use the identity (x2 x2 are the roots of the equation x2 x1)? = (x2 + x1)² X 1 and Rx + 4R = 0. 4x2x1 to find R. -
Transcribed Image Text:12 A particle is projected from the origin with speed V m/s at an angle a to the yA horizontal. a Assuming that the coordinates of the particle at time t are (Vt cos a, Vt sin a – ¿gt2), prove that the horizontal range R of the particle v² sin 2a is X2 6. b Hence prove that the path of the particle has equation y = x X tan a. R 1 - c Suppose that a = 45° and that the particle passes through two points 6 metres apart and 4 metres above the point of projection, as shown in the diagram. Let x, and x2 be the x-coordinates of the two points. i Show that ii Use the identity (x2 x2 are the roots of the equation x2 x1)? = (x2 + x1)² X 1 and Rx + 4R = 0. 4x2x1 to find R. -
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