5.2. Solved examples: Free Fall
Example 1
An object is thrown upwards with a velocity of [latex]25 \, \text{m/s}[/latex]
- Find the maximum height reached by the object.
- Find the time to reach the maximum height.
- Find the time the object was in flight.
Given:
[latex]v_i = 25 \, \text{m/s}[/latex]
[latex]v_f = 0 \, \text{m/s}[/latex]
[latex]g = 9.8 \, \text{m/s}^2[/latex]
[latex]v_i = 25 \, \text{m/s}[/latex]
[latex]v_f = 0 \, \text{m/s}[/latex]
[latex]g = 9.8 \, \text{m/s}^2[/latex]
Find:
[latex]\text{a) } h_{\text{max}} = ?[/latex]
[latex]\text{b) } t_{\text{up}} = ?[/latex]
[latex]\text{c) } t_{\text{total}} = ?[/latex]
[latex]\text{a) } h_{\text{max}} = ?[/latex]
[latex]\text{b) } t_{\text{up}} = ?[/latex]
[latex]\text{c) } t_{\text{total}} = ?[/latex]
Solution:
-
Decide which equation works to solve the question by examining what information is given and what needs to be found.[latex]v_f^2 = v_i^2 - 2gs[/latex]Rearrange the equation to express the wanted quantity:[latex]h_{\text{max}} = \frac{v_i^2}{2a}[/latex]Substitute the values for the known quantities in the last equation:[latex]h_{\text{max}} = \frac{v_i^2}{2a} = 31.9 \, \text{m} \approx 32 \, \text{m}[/latex]
Answer:
[latex]h_{\text{max}} = 32 \, \text{m}[/latex]
-
Choose the equation:[latex]v_f = v_i - gt[/latex]Rearrange the equation:[latex]t_{\text{up}} = \frac{v_i}{g}[/latex][latex]t_{\text{up}} = \frac{v_i}{g} = 2.55 \, \text{s} \approx 2.6 \, \text{s}[/latex]
Answer:
[latex]t_{\text{up}} \approx 2.6 \, \text{s}[/latex]
-
Since the object returns to the same level from which it started:[latex]t_{\text{up}} = t_{\text{down}}[/latex][latex]t_{\text{total}} = 2 \times t_{\text{up}} = 5.2 \, \text{s}[/latex]
Answer:
[latex]t_{\text{total}} = 5.2 \, \text{s}[/latex]
