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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