Finding minimum speed. . .

[racuna]

A golfer gives a ball a maximum initial speed of 39.5m/s. (Neglect air resistance.)

I found the longest possible hole in one for the golfer, which is 159.05m.

I need to find the minimum speed of the ball during the hole in one shot.
NO IDEA!!!

 

[TchrWill]

A golfer gives a ball a maximum initial speed of 39.5m/s. (Neglect air resistance.)

I found the longest possible hole in one for the golfer, which is 159.05m.

I need to find the minimum speed of the ball during the hole in one shot.

The ball will lose speed due too gravity pullig it down.
At the peak of its trajectory the vertical component of the ball's speed is zero.
The balls minimum speed will occur at the peak of its trajectory and will be equal to the horizontal component of the initial speed at impact of the ball.

The angle from the horiizontal, µ, of the ball's trajectory derives from d = V^2/g(sin2µ) hence sin2µ = 159.05(9.8)/(39.5^2) = .999 making 2µ = 87.437º and µ = 43.718º. The horizontal component of the initial speed is therefore Vh = 39.5(cos(43.718) = 28.548m/s, the slowest speed of the ball at the peak of its fl;ight which derives from h = V^2/2gsin^µ or h == 39.5^2/19.6(sin^2(43.718)) = 38m.