A stone is dropped from the upper observation deck of a tower, 850 m above the g

Question

A stone is dropped from the upper observation deck of a tower, 850 m above the ground. (Assume

g = 9.8 m/s2.)(a) Find the distance (in meters) of the stone above ground level at time t.

h(t) =

(b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.)
s

(c) With what velocity does it strike the ground? (Round your answer to one decimal place.)
m/s

(d) If the stone is thrown downward with a speed of 5 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)
s

Explanation / Answer

Consider the base of the tower at ground level to be the origin. a(t) is 9.8 regardless of time, so...

initial values
a(0) = -9.8??-negative because it accelerates down
v(0) = 0initially, the stone doesn't move when dropped
h(0) = 850

a(t) = -9.8

integrating from 0 to t will give you
v(t) = -9.8t + C ;v(0) = -9.8(0) + C = 0
v(t) = -9.8t , C = 0

integrating again will give you height above the ground
h(t) = -4.9t

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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