Question

You can run 9.8 m/s , 20% faster than your brother.

How much head start should you give him in order to have a tie race over 150 m ?
Express your answer to two significant figures and include the appropriate units.

Answer 1

You must give your brother a 3.05 seconds hear start.

Step-by-step explanation:

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:

`(9.8)/(x) =1.2\\ \\(x)/(9.8) =(1)/(1.2) \\ \\x=(9.8)/(1.2) \\ \\x=8.17`

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:

`D(t)=9.8(t)`

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:

`D(t)=8.17(t)`

4. Find out in how much time each person covers the 150 m.

a. Your time.

`9.8t=150=\\ \\t=(150)/(9.8)=\\\\ t=15.31`

b. Your brother's time.

`8.17t=150=\\ \\t=(150)/(8.17)=\\\\ t=18.36`

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:

`d=8.17(3.05)=\\ \\d=24.91 m`

Hence, you should give your brother a 24.91 meter head start.