Question

The gravitational force exerted on a baseball is `-F_ghatj`. A pitcher throws the ball, initially at rest, with velocity `v hat i` by uniformly accelerating it along a horizontal line for a time interval of `t`. What force does he exert on the ball?

Answer 1

Since motion along the directions `hatiand hatj` are orthogonal to each other these can be treated separately.

1. Force along `hati`
   Using Newtons Second Law of motion
   Mass of baseball `=F_g/g`
   Using the kinematic expression for uniform acceleration

   `v=u+at`
   Inserting given values we get
   `v=0+at`
   `=>a=v/t`
   `:.` Force `=F_g/gxxv/t`

2. Force along `hatj`
   It is given that there is no motion of the baseball in this direction. As such net force is `=0`
   `F_"net"=0=F_"applied"+(-F_g)`
   `=>F_"applied"=F_g`

Total force exerted by the pitcher on the ball `=(F_gv)/(g t)hati+F_ghatj`