A ballast is dropped from a stationary hot-air balloon that is hovering at an al

Question

A ballast is dropped from a stationary hot-air balloon that is hovering at an altitude of 300 ft. The velocity of the ballast after tsec is ?32t ft/sec.

A ballast is dropped from a stationary hot-air balloon that is hovering at an altitude of 300 ft. The velocity of the ballast after tsec is ?32t ft/sec. Find the height h(t) of the ballast from the ground at time t. Hint: h'(t) = ?32t and h(0) = 300. h(t) = ft When will the ballast strike the ground? (Round your answer to two decimal places.) Find the velocity of the ballast when it hits the ground. (Round your answer to two decimal places.)

Explanation / Answer

a)

h(t) = int h'(t) dt = -16t^2 + C -> h(0) = C = 300

therefore:

h(t) = 300 - 16t^2

b)

h(t) = 0 -> 16t^2 = 300 -> t = sqrt(300/16) = 4.33 s

c)

h'(t) = -32t = -32*4.33 = -138.56 ft/sec

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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