You can run 8.0 m/s , 20% faster than your brother. How much head start should you give him in order to have a tie race over 90 m ?

To solve this problem, we need to determine the speed of your brother and then calculate the head start you should give him.

Let's start by finding the speed of your brother. We are given that you can run 8.0 m/s, which is 20% faster than your brother's speed. To find your brother's speed, we need to subtract 20% from your speed.

First, let's calculate 20% of 8.0 m/s:
20% of 8.0 = (20/100) * 8.0 = 1.6 m/s

Now, subtract 1.6 m/s from 8.0 m/s to find your brother's speed:
8.0 m/s - 1.6 m/s = 6.4 m/s

Now that we know your brother's speed is 6.4 m/s, let's calculate the time it would take both of you to run 90 m. Since time equals distance over speed, we can use the formula:

Time = Distance / Speed

For you, the distance is 90 m and the speed is 8.0 m/s:
Time taken by you = 90 m / 8.0 m/s = 11.25 s

For your brother, the distance is also 90 m, but the speed is 6.4 m/s:
Time taken by your brother = 90 m / 6.4 m/s = 14.06 s

To have a tie race, your brother would need a head start of the time difference between you both.

Time difference = Time taken by you - Time taken by your brother
Time difference = 11.25 s - 14.06 s = -2.81 s

Note that the time difference is negative, indicating that your brother needs a head start before you start running.

Therefore, your brother would need a head start of 2.81 seconds in order to have a tie race over a distance of 90 meters.

how long do you take?

90 = 8 t
t = 11.25 seconds

8 = 1.20 v
v = 6.67 m/s
so
90 = 6.67 t
t = 13.5 s

so you should start 13.50 - 11.25
= 2.25 seconds after him