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A4) The point O is 8 m above a horizontal plane. A particle P is projected from 0. After projection, the horizontal and vertically upwards displacements of P from O are x m and y m, respectively. The equation of the trajectory of P is y = 2x - x? --(1). (i) Find the value of x for the point where P strikes the plane. (ii) Find the angle and speed of projection of P. (iii) Calculate the speed of P immediately before it strikes the plane.

A4) The point O is 8 m above a horizontal plane. A particle P is projected from 0. After projection, the horizontal and vertically upwards displacements of P from O are x m and y m, respectively. The equation of the trajectory of P is y = 2x - x? --(1). (i) Find the value of x for the point where P strikes the plane. (ii) Find the angle and speed of projection of P. (iii) Calculate the speed of P immediately before it strikes the plane.

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A4) The point O is 8 m above a horizontal plane. A particle P is projected from 0. After projection, the horizontal and vertically upwards displacements of P from O are x m and y m, respectively. The equation of the trajectory of P is y = 2x – x? ----(1). (i) Find the value of x for the point where P strikes the plane. Find the angle and speed of projection of P. (ii) Calculate the speed of P immediately before it strikes the plane. (ii) (i) y = 2x – x? : -8 = 2x – x² = x = 4 m (ii) Equation for trajectory: y = tan e x –: -- (2) 2v, cos? e = 0 = tan-(2) = 63.4° Comparing to (2) to (1): tan e = 2 and 2v cos? e = vo = 4.95 m/s = 1 (iii) v² = v3 – 2gy = 4.952 – 2(9.81)(-8) = v = 13.5 m/s = 181.485 %3D
Transcribed Image Text:A4) The point O is 8 m above a horizontal plane. A particle P is projected from 0. After projection, the horizontal and vertically upwards displacements of P from O are x m and y m, respectively. The equation of the trajectory of P is y = 2x – x? ----(1). (i) Find the value of x for the point where P strikes the plane. Find the angle and speed of projection of P. (ii) Calculate the speed of P immediately before it strikes the plane. (ii) (i) y = 2x – x? : -8 = 2x – x² = x = 4 m (ii) Equation for trajectory: y = tan e x –: -- (2) 2v, cos? e = 0 = tan-(2) = 63.4° Comparing to (2) to (1): tan e = 2 and 2v cos? e = vo = 4.95 m/s = 1 (iii) v² = v3 – 2gy = 4.952 – 2(9.81)(-8) = v = 13.5 m/s = 181.485 %3D
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