(4) When an object is dropped or thrown downward, the distance, in meters, that it falls in t seconds is given by the following formula:
s = 4.9t2 + vot
In this formula, vo is the initial velocity, in meters per
second. Use the above equation to answer the following questions.
(a) An object is dropped 75 m from an airplane. How long does it take
for the object to reach the ground?
(b) An object is thrown downward from the plane at an initial velocity
of 30 m/sec. How long does it take for the object to reach the ground?
(c) How far will an object fall in 2 sec if it is thrown downward at an
inital velocity of 30 m/sec?
SOLUTION:
(a) s = 4.9t2 + vot
75 = 4.9t2 + (0)t
t2 = 15.306
t = sqrt{15.306}
t = 3.91
It takes the object 3.91 sec to reach the ground.
(b) Here, vo = 30.
s = 4.9t2 + vot
75 = 4.9t2 + 30t
0 = 4.9t2 + 30t - 75
Using the quadratic formula, we get t = -8.03 and t = 1.91
Because t is a time value, the negative value of -8.03 is rejected.
Therefore, the object takes 1.91 sec to reach the ground.
(c) s = 4.9t2 + vot
s = 4.9(2)2 + (30)(2)
s = 19.6 + 60
s = 79.6 m
The object will fall 79.6 m.