Question

in a softball game, a batter hits the ball at the velocity of 27m/s and angle of 40. What is the maximum range of the ball?

Answer 1

Is it 27*40 to get the range?

Answer 2

kinematics equations in 2 dimensions.

consider the y-direction only first: vf = vi + at, where vf is 0 (at the top of the trajectory), vi is the initial velocity in the y-direction 27sin(40), a is the acceleration due to gravity (-9.81 m/s^2) and t is time. solve for t first.

since this represents the time to get to the peak of the trajectory, double this value to get the full time of flight.

then consider velocity in the x-direction only. multiply the x-direction velocity (27cos(40)) by the time from the previous step to get the horizontal range.