Question

table 2: heights and speeds of five identical planes
based on the data in the table, which two planes had the same kinetic energy but different potential energies when their heights and speeds were measured?
a) planes 1 and 2
b) planes 1 and 5
c) planes 3 and 4
d) planes 4 and 5

Explanation:

Step1: Recall the formulas

Kinetic energy formula \(KE=\frac{1}{2}mv^{2}\) (since planes are identical, \(m\) is the same, so \(KE\) depends on \(v\)). Potential energy formula \(PE = mgh\) ( \(m\) and \(g\) are the same, so \(PE\) depends on \(h\)).

Step2: Analyze kinetic energy

For kinetic energy:

• Plane 1: \(v = 1000\ km/h\)
• Plane 2: \(v=1100\ km/h\)
• Plane 3: \(v = 950\ km/h\)
• Plane 4: \(v = 950\ km/h\)
• Plane 5: \(v = 1000\ km/h\)

Planes 1 and 5 have the same speed (\(v = 1000\ km/h\)), so same \(KE\) (because \(KE\propto v^{2}\) for same - mass objects).

Step3: Analyze potential energy

For potential energy:

• Plane 1: \(h = 250\ m\)
• Plane 5: \(h = 500\ m\)

Since \(PE\propto h\) (for same - mass objects), planes 1 and 5 have different \(PE\)

Answer:

B. planes 1 and 5