A projectile is fired horizontally with a velocity u. obtainthe expression for resultant velocity of the projectile at any instant .

A projectile is fired horizontally with a velocity u. obtainthe expres

1.	A projectile is fired horizontally with a velocity u. obtainthe expression for resultant velocity of the projectile at any instant .
Answer» Solution :At any instant t, at the VELOCITY components of the projectile along both x-axis and y-axis. The resultant of these two components gives the velocity of the projectile at that instant t, as shown in the figure . The velocity COMPONENT at any instant of the t along horizontal (x-axis) is`v_(x) = u_(x) + a_(x)t` Since , `u_(x) = u, a_(x) = 0 ` , we get `v_(x) = u` the component of velocity along vertical DIRECTION (y-axis) is given by`v_(y) = u_(y) + a_(y) t` `v_(y) = g t` `:.`The velocity of the particle at any instant is `vec(v) = u hat(i) + g t hat(j)` The speed of the particle at any instant t is given by `:. v = sqrt(v_(x)^(2)+ v_(y)^(2))` `v = sqrt(u^(2) + g^(2) t^(2))`