A particle P is projected with speed 35ms^-1 from a point O on a horizontal plane. In the subsequent motion, the horizontal and vertically upwards displacements of P from O are x_m and y_m, respectively. The equation of the trajectory is

where k is a constant. P passes through the points A(14, a) and B(42, 2a), where a is a constant.

i. Calculate the two possible values of k and, hence, show that the larger of the two possible angles of projection is 63.435°, correct to 3 decimal places.

For the larger angle of projection, calculate

ii. The time after projection when P passes through A,

iii. The speed and direction of motion of P when it passes through B.

Transcribed Image Text:

(1 + k)x? y = kx - 245