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→Key Stage 4
Δh = The change in [[height]] of the [[object]].
===Calculating Change in Height from Gravitational Potential Energy===
{| class="wikitable"
| style="height:20px; width:200px; text-align:center;" |An [[object]] of [[mass]] 5.0kg is lifted increasing its '''gravitational potential energy''' by 245J. Calculate the change in [[height]] of the [[object]].
[[Gravitational Field Strength]] on [[Earth]] is 9.8N/kg.
| style="height:20px; width:200px; text-align:center;" |A 3.6kg [[cat]] jumps [[vertical]]ly with an initial [[Kinetic Energy Store|kinetic energy]] of 70J. Calculate the maximum [[height]] that the [[cat]] will be able to reach in this jump correct to two [[Significant Figures|significant figures]].
[[Gravitational Field Strength]] on [[Earth]] is 9.8N/kg.
| style="height:20px; width:200px; text-align:center;" |A vacationing [[astronaut]] takes a bow and arrow to [[The Moon]]. The bow has an initial [[Elastic Potential Energy Store|elastic potential energy store]] of 400J before releasing the arrow [[vertical]]ly. Given the [[mass]] of the arrow is 120g; calculate the maximum [[height]] that the arrow will reach before returning to the ground correct to two [[Significant Figures|significant figures]].
[[Gravitational Field Strength]] on [[Earth]] is 1.6N/kg.
|-
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 5.0kg
g = 9.8N/kg
E<sub>g</sub> = 245J
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 3.6kg
g = 9.8N/kg
E<sub>g</sub> = 70J (Since the law of [[Conservation of Energy]] states that [[energy]] is [[Energy Transfer|transferred]] from one [[Energy Store|store]] into another.)
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 120g = 0.12kg
g = 1.6N/kg
E<sub>g</sub> = 400J (Since the law of [[Conservation of Energy]] states that [[energy]] is [[Energy Transfer|transferred]] from one [[Energy Store|store]] into another.)
|-
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>E_g = m g \Delta h</math>
<math>245 = 5 \times 9.8 \times h</math>
<math>245 = 49h</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>E_g = m g \Delta h</math>
<math>70 = 3.6 \times 9.8 \times h</math>
<math>70 = 35.28h</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>E_g = m g \Delta h</math>
<math>400 = 0.12 \times 1.6 \times h</math>
<math>400 = 0.192h</math>
|-
| style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>h = \frac{245}{49}</math>
<math>h = 5m</math>
| style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>h = \frac{70}{35.28}</math>
<math>h = 1.984127m</math>
<math>h \approx 2.0m</math>
| style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>h = \frac{400}{0.192}</math>
<math>h = 2083.3m</math>
<math>h \approx 2100m</math>
|}