Question

a golfer hits a ball onto a green at the top of a hill and it follows the trajectory shown in the image below. note: point a is after the ball has been hit. fill in the blanks by selecting one option from each menu. part 1: 2 points part 2: 2 points part 3: 2 points part 4: 2 points part 5: 2 points 10 points at what point does the ball have the highest potential energy? -- at what point does the ball have the highest kinetic energy? -- at what point does the ball have the lowest potential energy? -- at what point does the ball have the lowest kinetic energy? -- the total energy of the golf ball at point b is -- the total energy of the golf ball at point c. (assume no energy loss due to air resistance.)

Explanation:

• Potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height). Higher \(h\) means higher \(U\). Point \(C\) is the highest, so highest potential energy at \(C\).
• Kinetic energy \(K=\frac{1}{2}mv^{2}\). At point \(A\), the ball is just hit (assuming no height gain yet compared to \(D\) in terms of speed - initial velocity is maximum as it starts the motion, so highest \(K\) at \(A\)).
• Lowest \(h\) gives lowest \(U\). Point \(D\) is at the lowest height (on the green), so lowest potential energy at \(D\).
• At the highest point (\(C\)), vertical component of velocity is \(0\) (in projectile - like motion, at peak vertical speed \(v_y = 0\), and speed is minimum there compared to other points), so lowest kinetic energy at \(C\).
• By conservation of mechanical energy (since no air resistance, \(E = K + U\) is constant). So total energy at \(B\) is equal to total energy at \(C\).

Answer:

• Highest potential energy: \(C\)
• Highest kinetic energy: \(A\)
• Lowest potential energy: \(D\)
• Lowest kinetic energy: \(C\)
• Total energy comparison (\(B\) and \(C\)): equal to