Answer:
38.559 meters
Step-by-step explanation:
Let the distance traveled along shore before the jump be "x"
meters
time take during run: speed = distance / time therefore time = distance / speed, i.e .:
x / 4
Now the distances are:
40
50 - x
a right triangle is formed so it is possible to use Pythagoras:
d ^ 2 = 40 ^ 2 + (50 - x) ^ 2
d = [40 ^ 2 + (50 - x) ^ 2] ^ (1/2)
time taken during swin:
[40 ^ 2 + (50 - x) ^ 2] ^ (1/2) /1.1
total time:
x / 4 + [40 ^ 2 + (50 - x) ^ 2] ^ (1/2) /1.1
we derive and we are left:
1/4 - (1 / 1.1) * (50-x) / [40 ^ 2 + (50 - x) ^ 2] ^ (1/2)
we equal 0:
1/4 - (1 / 1.1) * (50-x) / [40 ^ 2 + (50 - x) ^ 2] ^ (1/2) = 0
1.1 * [40 ^ 2 + (50 - x) ^ 2] ^ (1/2) = 4 * (50 -x)
we square both sides:
1.21 * (40 ^ 2 + (50 - x) ^ 2 = 16 * (50 -x) ^ 2
1936 + 1.21 * (50-x ^ 2) = 16 * (50 -x) ^ 2
1936 = 14.79 * (50 -x) ^ 2
(50 -x) ^ 2 = 1936 / 14.79
(50 -x) ^ 2 = 130.9
50 - x = + -11.441
x = 50 + - 11.441
x1 = 50 + 11.441 = 61.441
x2 = 50 - 11.441 = 38.559
x1 cannot be because it is greater than 50 - x, the result would be negative, therefore the answer is x = 38.559 meters
