You must give your brother a 3.05 seconds hear start.
1. Find out how fast is your brother.
If you are 20% faster than your brother, it means that when you divide your speed by the speed of your brother, the result if 1.2. Let x be the speed of your brother. Hence:
[tex]\frac{9.8}{x} =1.2\\ \\\frac{x}{9.8} =\frac{1}{1.2} \\ \\x=\frac{9.8}{1.2} \\ \\x=8.17[/tex]
2. Find an equation of your velocity.
Let D(t) be the distance you travel.
Let x be the time is takes to travel that distance.
Hence, your distance, with respect to time, is given by:
[tex]D(t)=9.8(t)[/tex]
3. Find an equation of your brother's velocity.
Let D(t) be the distance you travel.
Let x be the time is takes to travel that distance.
Hence, your brother's distance, with respect to time, is given by:
[tex]D(t)=8.17(t)[/tex]
4. Find out in how much time each person covers the 150 m.
a. Your time.
[tex]9.8t=150=\\ \\t=\frac{150}{9.8}=\\\\ t=15.31[/tex]
b. Your brother's time.
[tex]8.17t=150=\\ \\t=\frac{150}{8.17}=\\\\ t=18.36[/tex]
5. Find the difference in times.
Δt= 18.36-15.31= 3.05 seconds.
6. Express your answer.
You must give your brother a 3.05 seconds hear start.
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If you would to express the answer in meters, do the following:
[tex]d=8.17(3.05)=\\ \\d=24.91 m[/tex]
Hence, you should give your brother a 24.91 meter head start.
