Extended-Answer Questions 3. 120] (Thi s problem is based on a true story) In 20

Question

Extended-Answer Questions 3. 120] (Thi s problem is based on a true story) In 2016, skydiver Luke Aikins jumped without a parachute from an airplane at 25000 feet (7600 m) and landed in a giant horizontal net suspended roughly 80 ft (24 m) above the ground. The net, which can be modeled as a spring, slowed him to a stop. (Assume his mass was 75 kg. (a) Ignoring air resistance, and assuming that gravity was constant up to his starting height, find his speed just before hitting the net. (b) Determine the spring constant of the net. (c) In reality air resistance would have limited his fall speed to roughly 120 mi/hr, or 54 m/s (known as "terminal velocity"). Determine the spring constant of the net in this case. (Note that all estimated numbers in this problem are given to only two significant figures.)

Explanation / Answer

Given,

h = 7600 m ; h' = 24 m ; x = 12 m ; m = 75 kg

a)from conservation of energy

1/2 m v^2 = m g H

v = sqrt (2 g H)

H = h - h' = 7600 - 24 = 7576 m

v = sqrt (2 x 9.81 x 7576) = 385.54 m/s

Hence, v = 385.54 m/s

b)The Hook's force and weight balanced so

m g = k x => k = mg/x = 75 x 9.81/12 = 61.31 N/m

Hence, k = 61.31 N/m

[conservation of energy gives us,1/2 k x^2 = m g x => k = 2 mg/x = 2 x 75 x 9.81/12 = 122.63 N/m]

c)vt = 54 m/s

from conservation of energy

1/2 m v^2 = 1/2 k x^2

k = v/x sqrt(m)

k = 54/12 sqrt(75) = 38.97 N/m

Hence, k = 38.97 N/m

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.