A ball is projected horizontally in air such that it moves with a constnat horizontal accelration a due to air flow. Taking the gravitational acelration into account. Find the (a) velocity (b) accelration as the function of time till it strikes the ground.

Explanation

Here `a_(x)=a,a_(y)=-g` and `v_(0x)=v_(0)` and `v_(0)y=0`.
The velocity components are
`v_(x)=v_(0x)+a_(x)t`
or `v_(x)=v_(0)+at`
`v_(y)=0+(-g)t`
or `v_(y)=-g t`
Then, `v=v_(x)hati+v_(y)hatj`
The displacemnet components are
`Deltax=x=v_(0x)t+(1)/(2)a_(x)t^(2)`
or `x=v_(0)t+(1)/(2)at^(2)`
`Deltay=y=v_(0)yt+(1)/(2)a_(y)t^(2)`
or `y=-(1)/(2)g t^(2)`
Then, the net displacement is
`vecs=vecr=(v_(0)t+(1)/(2)omegat^(2))hati-(1)/(2)g t^(2)hatj`