You can run 8.8m/s,20% faster than your brother. How much head start should you give him in order to have a tie race over 110m?please help:(
r1 = 8.8 m/s = Your speed.
r2 = 0.8 * 8.8 = 7.04 m/s = Your bro. speed.
8.8t = 110
t = 12.5 s
7.04t = 110-d
7.04*12.5 = 110-d
d = 110-88 = 22 m. Head start.
To determine the head start you should give your brother for a tie race, we first need to find out your brother's speed.
Given that you can run at a speed of 8.8 m/s, which is 20% faster than your brother, we can calculate your brother's speed by reducing your speed by 20%.
Let's find your brother's speed:
20% of 8.8 m/s = (20/100) * 8.8 m/s = 1.76 m/s
To find your brother's speed, we subtract 1.76 m/s from your speed:
8.8 m/s - 1.76 m/s = 7.04 m/s
So your brother's speed is 7.04 m/s.
Now, since we want to have a tie race, we need to determine the time it takes for both of you to cover the same distance of 110m.
Using the formula: time = distance / speed
Your time to cover 110m can be calculated as:
time = 110m / 8.8 m/s = 12.5 seconds
Your brother's time to cover the same distance is:
time = 110m / 7.04 m/s = 15.63 seconds
To have a tie race, you need to give your brother a head start equal to the time difference between your times.
Time difference = YOUR time - BROTHER's time = 12.5 seconds - 15.63 seconds = -3.13 seconds
The negative value indicates that you finish earlier than your brother. Therefore, no head start is needed in this case. You can simply start at the same time, and it will result in a tie race.