A particle is moving in XY-plane as such at any time t ,vx=(50 - 16 t ) m/s and vy=-8t m/s. Initially the particle was at point (0,100 m).The equation of trajectory of the particle is The speed of particle at y = 0 is The magnitude of acceleration of particle at y = 0 is

vx=50−16t  or  dxdt=50−16tor ∫0x dx=50∫0t dt−16∫0t tdtor x−0=50t−16t22 or x=50t−8t2 and ∫100y1dy=∫0t-8tdt⇒ y=100−4t2 or  4t2=100−y or t2=25−y4∴ t=25−y4∴ x=50t−825−y4 or  x=50t−200+2y or  x=5025−y/4−200+2y or (x−2y+200)2=250025−y4∵y=100−4t2 or 0=100−4t2 or  t2=25∴ t=5s∵     y=100−4t2or     vy=dydt=−8t=−8×5=−40ms−1and   vx=50−16t=50−16×5=−30ms−1∴  Speed =vx2+vy2=50ms−1ax=dvxdt=−16ms−2⇒ay=dvydt=−8ms−2∴ a=ax2+ay2=17.9ms−2