A golfer plays a putt stroke on a level green (fine grass surface), hitting ball

Question

A golfer plays a putt stroke on a level green (fine grass surface), hitting ball A toward the hole. She strikes the ball perfectly, giving it just the right initial speed V so that after slowing on the grass, the ball just reaches the hole and falls into it. Her partner's ball B lies exactly twice as far from the hole. In order for ball B to just reach the hole, at what speed must be traveling immediately after being struck? Assume a constant retarding force on the grass. please show me the steps.

Explanation / Answer

Here,

as the acceleration of both ball will be same

let the distance is d

V^2 - 0^2 = 2 * a * d

a = V^2/(2d)

Now, for the second partner

the distance will be 2d

now , for the velocity is v1

v1^2 = 2 * a * 2d

v1^2 = 2 * V^2/(2d) * 2d

v1^2 = 2 * V^2

v1 = sqrt(2)*V

the speed needed is sqrt(2)*V

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