HARRY GIVES SAM A 30m head start in 100m dash. Harry can run 10m/s, while sam only runs 6.0 m/s per second, how much of a head start does sam need to win!
also guys please explain how to do it, and explain the formula and the reasons behind why, I'm here to learn thanks!
To determine how much of a head start Sam needs to win, we can first calculate how long it takes for both Harry and Sam to finish the race.
Let's assume Sam needs a head start of "x" meters.
Harry's time to finish the race (T_harry) can be calculated using the formula:
T_harry = Distance / Speed = (100m - x) / 10m/s
Sam's time to finish the race (T_sam) can be calculated using a similar formula:
T_sam = Distance / Speed = 100m / 6.0m/s
For Sam to win the race, his time (T_sam) must be less than Harry's time (T_harry).
So, we can set up the equation:
T_sam < T_harry
100m / 6.0m/s < (100m - x) / 10m/s
Now, let's solve the inequality to find the range of "x" values for Sam to win.
100m / 6.0m/s < (100m - x) / 10m/s
Simplifying the inequality:
16.67s < (10s - x/10s)
Multiplying through by 10 to remove the denominators:
166.67 < 10 - x/10
Adding x/10 to both sides:
166.67 + x/10 < 10
Subtracting 10 from both sides:
x/10 < 10 - 166.67 = -156.67
Multiplying through by 10 to remove the denominator:
x < -1566.7
Since the distance of a race cannot be negative, it means there is no head start that would allow Sam to win the race if Harry runs 10m/s and Sam runs 6.0m/s. Harry will always finish the race faster.