Final answer:
The net would stretch 98 cm if the same person were lying in it.
Step-by-step explanation:
The question states that a person jumps from a window to a fire net 20.6 m below, which stretches the net 1.0 m. We are asked to calculate how much the net would stretch if the same person were lying in it.
To solve this problem, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to the amount it stretches or compresses. In this case, the weight of the person exerts a force on the net, causing it to stretch.
We can calculate the net's stretch using the equation F = kx, where F is the force exerted by the net, k is the spring constant, and x is the stretch of the net. Rearranging the equation, we get x = F/k.
Since we are given the weight of the person (61 kg) and the stretch of the net (1.0 m), we can calculate the force exerted by the net using the equation F = mg, where m is the mass of the person and g is the acceleration due to gravity (9.8 m/s²). Substituting the values, we find that F = 61 kg × 9.8 m/s² = 598.8 N.
To find the spring constant k, we can rearrange the equation x = F/k to get k = F/x. Substituting the values, we find that k = 598.8 N / 1.0 m = 598.8 N/m.
Now, we can use the spring constant k to find the stretch x if the same person were lying in the net. Rearranging the equation x = F/k, we find that x = F / (k * m), where m is the mass of the person. Substituting the values, we get x = 598.8 N / (598.8 N/m * 61 kg) = 0.98 m = 98 cm.