A projectile shot at a angle of 45^(@) above the horizontal strikes a building 30 m away at a point 15 m above the point of projection. Find a. the speed of projection(b) the magnitude and direction of velocity of projectile when it strikes the building.

A projectile shot at a angle of 45^(@) above the horizontal strikes a

1.	A projectile shot at a angle of 45^(@) above the horizontal strikes a building 30 m away at a point 15 m above the point of projection. Find a. the speed of projection(b) the magnitude and direction of velocity of projectile when it strikes the building.
Answer» Solution :Let u is the speed of projection a. Let P be the point on the building wher projectile hits it. Taking point of projection as origin COORDINATES of P are (30,15) Using the equation of trajectory. `y=xtan THETA-(gx^(2))/(2u^(2)cos^(2)theta)implies15=30tan45^(@)-(g(3)^(2))/(2u^(2)cos^(2)45^(@))impliesu=24.2ms^(-1)` b. At `p,v_(x)=u_(x)=24.2cos 45^(@)=17.11ms^(-1)` `v_(y)^(2)=u_(y)^(2)+2a_(y)s_(y)impliesv_(y)^(2)=u^(2)sin^(2)45^(@)-2g(15)` `v_(y)^(2)=(60g)(0.5)-30g=0impliesv_(y)=0` At P projectile is at its highest point and hence moving horiontally.