Answer
See answers.
Work Step by Step
Start with the “uphill lie,” putting down the hill. Let the positive direction be the direction of the putt. The final velocity of the ball is 0, and the acceleration of the ball is $-1.8m/s^2$.
Use equation 2-11c to find the initial velocity.
$$v_0=\sqrt{v^2-2a(x-x_0)}$$
For the ball to be 1.0 m short or long, the displacements are 6.0 m or 8.0 m.
$$v_0=\sqrt{0^2-2(-1.8m/s^2)(6.0m)}=4.65m/s$$
$$v_0=\sqrt{0^2-2(-1.8m/s^2)(8.0m)}=5.37m/s$$
The range of acceptable velocities for the uphill lie is 5.37-4.65 = 0.72 m/s.
Now analyze the “downhill lie,” putting up the hill. Let the positive direction be the direction of the putt. The final velocity of the ball is 0, and the acceleration of the ball is $-2.6m/s^2$.
Use equation 2-11c to find the initial velocity.
$$v_0=\sqrt{v^2-2a(x-x_0)}$$
For the ball to be 1.0 m short or long, the displacements are 6.0 m or 8.0 m.
$$v_0=\sqrt{0^2-2(-2.6m/s^2)(6.0m)}=5.59m/s$$
$$v_0=\sqrt{0^2-2(-2.6m/s^2)(8.0m)}=6.45m/s$$
The range of acceptable velocities for the downhill lie is 6.45-5.59 = 0.86 m/s.
More control is necessary to putt downhill (the "uphill lie") because the range is smaller.
