A golfer misjudges a putt and leaves her ball way short, the ball going only one-third of the way to the hole. If the speed of the ball leaving the putter in the first case was v₀ 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?

Question

Quizplus · Accepted Answer

This question is dealing with the conservation of energy. When the ball is putted, it has some initial kinetic energy. As the ball moves towards the hole, the grass exerts a constant force in the opposite direction, causing the ball to slow down. However, the force of resistance does not change the total mechanical energy of the system. Therefore, the initial kinetic energy of the ball is converted into potential energy as it rises to a certain height, and then back into kinetic energy as it falls into the hole. Let's assume the mass of the ball is m, and the height of the hole is h. We can write the conservation of energy equation as: (1/2)mv₀^2 = mgh + (1/2)mvF1U1B10F1U1B0^2 Where g is the acceleration due to gravity, vF1U1B10F1U1B0 is the final velocity of the ball when it falls into the hole, and we want to solve for v₀, the initial velocity of the ball. We know that the ball only travels one-third of the way, so the distance it travels can be written as d = (1/3)h. We can express vF1U1B10F1U1B0 in terms of v₀ by using the equations of motion: vF1U1B10F1U1B0^2 = v₀^2 - 2ad where a is the acceleration due to the force of resistance, which is constant. Substituting d = (1/3)h and a = F/m, we get: vF1U1B10F1U1B0^2 = v₀^2 - 2(F/m)(1/3)h Now we can substitute this expression into the conservation of energy equation: (1/2)mv₀^2 = mgh + (1/2)mv₀^2 - Fh/3m Simplifying and solving for v₀, we get: v₀ = sqrt((5/3)gh) Since h and g are constants, we see that v₀ is proportional to the square root of h, which means we need to choose an answer that is slightly more than the original speed of the ball. The only answer choice that satisfies this is C, which is v₀ .

A Golfer Misjudges a Putt and Leaves Her Ball Way