Answer
The correct answer is: (d)
Work Step by Step
The golf ball begins its upward climb with a kinetic energy of $\frac{1}{2}mv_0^2$. At the ground, the initial gravitational potential energy is zero. As the height increases, the kinetic energy is gradually converted into gravitational potential energy until the gravitational potential energy reaches its maximum value when the ball is at maximum height.
On the way down, the gravitational potential energy decreases as the gravitational potential energy is converted back into kinetic energy.
We can find an equation for the vertical position as a function of time:
$y = v_0~t+\frac{1}{2}a_y~t^2$
$y = -4.9~t^2+v_0~t$
We can find an expression for the gravitational potential energy as a function of time.
$U = mgy$
$U = -(4.9mg)~t^2+(v_0~mg)~t$
This is the equation of a parabola that is concave down. Note that $U = 0$ at time $t = 0$.
The correct answer is: (d)
