You throw a baseball straight upward. The drag force is proportional to v2. In terms of g, what is the y-component of the ball’s acceleration when the ball’s speed is half its terminal speed and (a) it is moving up? (b) It is moving back down?
Solution 40E Step 1 of 5: 2 The drag force, f = Dv Weight, W= mg Where m is the mass of the ball and g is acceleration due to gravity. Using newton’s law, Force along vertical direction(y-component), F= ma=Dv ± mg ……………..1 Depending on whether the ball is moving up or down. Step 2 of 5: At equilibrium, drag force equals the weight Dv = mg v = mg D mg v = D Since we have to find at half of the terminal velocity, v = 2 v = 1 mg 2 D v = mg 4D 2 mg v = 4D Using in equation 1, F= ma=D( mg ) ± mg 4D F= ma=( mg) ± mg 4 Step 3 of 5: Solving for horizontal component of acceleration, g ma =m(( )4± g ) g a=(( 4 ± g )..............................2