# Range of a baseball ball

A baseball player hits the baseball with a velocity of 63 m/s at an angle of 22 degrees with the ground. What is the range of the baseball?

First, one needs to find the x (horizontal) and y (vertical) components of the speed.

$Vx = V*cos(\alpha) =63*cos(22) = 58.41 m/s$

$Vy = V*sin(\alpha) =63*sin(22) =23.60 m/s$

The time t1 to the maximum altitude comes from (at maximum amplitude the vertical speed is zero)

$0 = Vy-g*t1$

$t1 =Vy/g =23.60/9.81 = 2.40 seconds$

Total time of flight is (the trajectory is simetric on ascending and descending parts)

$t_{tot} = 2*t1 =2.4*2 =4.8 seconds$

Total horizontal distance (range) is

$x_{max} =vx*t_tot =58.41*4.8 =281.03 m$