A golfer misjudges a putt and leaves her ball way short, the ball going only half of the way to the hole. If the speed of the ball leaving the putter in the first case was vo and the force of resistance due to the grass remains the same, what speed should she have given to the ball to make the original putt?

Using

1/2mv^2 = work done by friction

work done = force x distance

lets call the force 3 N

lets call v = 3 m/s

lets call mass = 2 kg

0.5 x 2 x 3^2 = 9 J

9/3N = 3 m/s

now times 3 m/s by square root of 2 of which is 1.4142

3 x 1.4142= 4.2426 m/s

0.5 x 2 x 4.2426^2 = 18

18/2N = 9 m

a.) travels faster in solids because the particles are closer together.

air is a gas water is a liquid