B and c only 12 A particle is projected from the origin with speed V m/s at an angle a to theyAhorizontal.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 particlev² sin 2aisX26.b Hence prove that the path of the particle has equation y = xXtan a.R1 -c Suppose that a = 45° and that the particle passes through two points 6metres apart and 4 metres above the point of projection, as shown in the diagram. Let x, and x2 be thex-coordinates of the two points.i Show thatii Use the identity (x2x2 are the roots of the equation x2x1)? = (x2 + x1)²X 1andRx + 4R = 0.4x2x1 to find R.-

Name: B and c only 12 A particle is projected from the origin with speed V m
Uploaded: 2024-03-05T11:56:34.000Z
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Description: B and c only 12 A particle is projected from the origin with speed V m/s at an angle a to theyAhorizontal.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 particlev² si

Given that: Coordinate at any time t: (Vtcosα, Vtsinα-12gt2)

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A particle is projected from the origin with speed V m/s at an angle a to the norizontal. 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 *(1 - Jun 6 b Hence prove that the path of the particle has equation y = x 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-coordinates of the two points. and x2 be the i Show that x1 and x2 are the roots of the equation x2 ii Use the identity (x2 - x1)? = (x2 + x1) - 4xx¡ to find R. Rx + 4R = 0.