ella has a mass of 56 kg, and tyrone has a mass of 68 kg. ella is standing at the top of a skateboard ramp that is 1.5 meters tall. which conclusion is best supported by the given information?
- if tyrone stands at the top of the same ramp, his potential energy will be less than ella’s.
- if tyrone stands at the top of a 1 m high ramp, his potential energy will be greater than ella’s.
- if tyrone stands at the top of the same ramp, his potential energy will be the same as ella’s.
- if tyrone stands at the top of a 2 m high ramp, his potential energy will be greater than ella’s.

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To solve this, we use the formula for gravitational potential energy: $ PE = mgh $, where $ m $ is mass, $ g $ is acceleration due to gravity (constant), and $ h $ is height. ### Analyzing each option: - **Option 1**: Same ramp ($ h $ same), Tyrone’s mass ($ 68 \, \text{kg} $) > Ella’s ($ 56 \, \text{kg} $). Since $ PE \propto m $ (when $ h $ and $ g $ are constant), Tyrone’s $ PE $ should be **greater** than Ella’s. So this is incorrect. - **Option 2**: Tyrone on a $ 1 \, \text{m} $ ramp, Ella on $ 1.5 \, \text{m} $ ramp. Tyrone’s $ m = 68 $, $ h = 1 $; Ella’s $ m = 56 $, $ h = 1.5 $. Calculate $ PE $: - Tyrone: $ PE_T = 68 \times g \times 1 = 68g $ - Ella: $ PE_E = 56 \times g \times 1.5 = 84g $ $ 68g < 84g $, so Tyrone’s $ PE $ is less. But let’s check other options. - **Option 3**: Same ramp ($ h = 1.5 \, \text{m} $)? Wait, no—this option says “1 m high ramp” for Tyrone, but Ella’s ramp is $ 1.5 \, \text{m} $. Wait, re-reading: The original ramp is $ 1.5 \, \text{m} $ (Ella’s). Option 3 says “Tyrone stands at the top of the same ramp” (so $ h = 1.5 \, \text{m} $)? Wait, no, the option text is: *“If Tyrone stands at the top of a 1 m high ramp, his potential energy will be greater than Ella’s.”* Wait, no—let’s re-express: Wait, the original problem: Ella is on a $ 1.5 \, \text{m} $ ramp. Let’s re-express each option with $ PE = mgh $: - **Option 1**: Same ramp ($ h = 1.5 \, \text{m} $), Tyrone ($ m = 68 $), Ella ($ m = 56 $). $ PE_T = 68 \times g \times 1.5 $, $ PE_E = 56 \times g \times 1.5 $. Since $ 68 > 56 $, $ PE_T > PE_E $. So Option 1 is wrong (it says “less than”). - **Option 2**: Tyrone on $ 1 \, \text{m} $ ramp: $ PE_T = 68 \times g \times 1 = 68g $. Ella on $ 1.5 \, \text{m} $ ramp: $ PE_E = 56 \times g \times 1.5 = 84g $. $ 68g < 84g $, so Tyrone’s $ PE $ is less. But let’s check Option 4. - **Option 3**: Wait, the third option’s text: *“If Tyrone stands at the top of the same ramp, his potential energy will be the same as Ella’s.”* Same ramp ($ h = 1.5 \, \text{m} $), different masses. $ PE \propto m $, so different $ PE $. Wrong. - **Option 4**: Tyrone on $ 2 \, \text{m} $ ramp: $ PE_T = 68 \times g \times 2 = 136g $. Ella on $ 1.5 \, \text{m} $ ramp: $ PE_E = 56 \times g \times 1.5 = 84g $. $ 136g > 84g $, so Tyrone’s $ PE $ is greater. Wait, but let’s re-examine the options. The key is to find which conclusion is **best supported**. Let’s re-express all: 1. Same ramp ($ h = 1.5 \, \text{m} $): $ PE_T = 68 \times g \times 1.5 = 102g $ $ PE_E = 56 \times g \times 1.5 = 84g $ So $ PE_T > PE_E $. So Option 1 (says “less than”) is wrong. 2. Tyrone on $ 1 \, \text{m} $: $ PE_T = 68g $; Ella on $ 1.5 \, \text{m} $: $ PE_E = 84g $. $ 68g < 84g $, so Tyrone’s $ PE $ is less. This is true, but let’s check Option 4. 3. Same ramp: $ PE_T eq PE_E $ (different masses), so wrong. 4. Tyrone on $ 2 \, \text{m} $: $ PE_T = 68 \times g \times 2 = 136g $; Ella on $ 1.5 \, \text{m} $: $ PE_E = 56 \times g \times 1.5 = 84g $. $ 136g > 84g $, so this is true. But which is “best supported”? Let’s check the options again. The original ramp is $ 1.5 \, \text{m} $ (Ella’s). Let’s re-express the options: - Option 1: Same ramp (1.5m) → Tyrone’s PE < Ella’s? No, 68>56, so PE_T > PE_E. Wrong. - Option 2: Tyrone on 1m, Ella on 1.5m → PE_T = 68g, PE_E=84g → PE_T < PE_E. True, but let’s check Option 4. - Option 3: Same ramp → PE same? No, different masses. Wrong. - Option 4: Tyrone on 2m, Ella on 1.5m → PE_T = 136g, PE_E=84g → PE_T > PE_E. True. Wait, but the question is which conclusion is **best supported**. Let’s check the logic: Potential energy depends on mass and height ($ PE = mgh $). - For Option 2: Tyrone’s height is less (1m vs. 1.5m), but his mass is greater (68 vs. 56). Let’s calculate the ratio: $ \frac{PE_T}{PE_E} = \frac{68 \times 1}{56 \times 1.5} = \frac{68}{84} \approx 0.81 $, so PE_T < PE_E. - For Option 4: Tyrone’s height is greater (2m vs. 1.5m), and mass is greater. $ \frac{PE_T}{PE_E} = \frac{68 \times 2}{56 \times 1.5} = \frac{136}{84} \approx 1.62 $, so PE_T > PE_E. But the question is which conclusion is “best supported”. Let’s check the options again. The key is that in Option 4, both mass and height of Tyrone are greater (mass: 68>56, height: 2>1.5), so his PE must be greater. In Option 2, height is less, so even with greater mass, PE is less. But the question is which is “best supported”. Let’s re-express the options: Wait, the original problem’s ramp for Ella is 1.5m. Let’s check each option: 1. Same ramp (1.5m): Tyrone’s PE < Ella’s? No, 68>56, so PE_T > PE_E. Wrong. 2. Tyrone on 1m: PE_T > PE_E? No, 68*1=68, 56*1.5=84, so 68<84. So PE_T < PE_E. So this is true, but let’s check Option 4. 3. Same ramp: PE same? No. Wrong. 4. Tyrone on 2m: PE_T > PE_E? 68*2=136, 56*1.5=84. 136>84. So this is true. Now, which is “best supported”? The question is about which conclusion is best supported. Let’s see the options: - Option 2: Tyrone on 1m (lower height) has PE less than Ella on 1.5m. This is true, but Option 4: Tyrone on 2m (higher height) has PE greater than Ella on 1.5m. This is also true. Wait, maybe I misread the options. Let me recheck the original image: The options are: 1. If Tyrone stands at the top of the same ramp, his potential energy will be less than Ella’s. 2. If Tyrone stands at the top of a 1 m high ramp, his potential energy will be greater than Ella’s. 3. If Tyrone stands at the top of the same ramp, his potential energy will be the same as Ella’s. 4. If Tyrone stands at the top of a 2 m high ramp, his potential energy will be greater than Ella’s. Ah! I made a mistake earlier. Option 2 says “greater than”, but in reality, for Option 2: $ PE_T = 68 \times g \times 1 = 68g $, $ PE_E = 56 \times g \times 1.5 = 84g $. So $ 68g < 84g $, so Option 2 is false (it claims “greater than”). Option 4: $ PE_T = 68 \times g \times 2 = 136g $, $ PE_E = 56 \times g \times 1.5 = 84g $. $ 136g > 84g $, so this is true. So correcting: - Option 1: Same ramp (1.5m). $ PE_T = 68 \times 1.5 \times g = 102g $, $ PE_E = 56 \times 1.5 \times g = 84g $. So $ PE_T > PE_E $. But Option 1 says “less than”—false. - Option 2: Tyrone on 1m. $ PE_T = 68 \times 1 \times g = 68g $, $ PE_E = 56 \times 1.5 \times g = 84g $. $ 68g < 84g $, but Option 2 says “greater than”—false. - Option 3: Same ramp. $ PE_T eq PE_E $—false. - Option 4: Tyrone on 2m. $ PE_T = 68 \times 2 \times g = 136g $, $ PE_E = 56 \times 1.5 \times g = 84g $. $ 136g > 84g $—true. Thus, the correct answer is the fourth option: *If Tyrone stands at the top of a 2 m high ramp, his potential energy will be greater than Ella’s.* # Answer: D. If Tyrone stands at the top of a 2 m high ramp, his potential energy will be greater than Ella’s. (Assuming the options are labeled A-D as per typical multiple-choice; if the original labels are different, adjust accordingly. Based on the text, the fourth option is correct.)

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