Classical Mechanics (Kibble & Berkshire) · Problem 4.36

Linear oscillations — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · computer-assisted-baseball-trajectory

Problem

Baseball trajectory A baseball is struck with an initial speed of

45\text{ m s}^{-1}

(just over 100 mph) at an elevation angle of

40^\circ

. Find its path and compare this with the corresponding path when air resistance is neglected. [A baseball has mass 0.30 kg and radius 3.5 cm. Assume the quadratic law of resistance.] Show that the equation of motion can be written in the form

\frac{d\boldsymbol{v}}{dt} = -g\left(\boldsymbol{k} + \frac{\boldsymbol{v}|\boldsymbol{v}|}{V^2}\right),

where

V

is the terminal speed. Resolve this vector equation into two (coupled) scalar equations for

v_x

and

v_z

and perform a numerical solution. In this example, air resistance reduces the range by about 35\%. It really is easier to hit a home run in Mile High stadium!

Browse the problem library