Consider the following descriptions of the vertical motion of an object subject

Question

Consider the following descriptions of the vertical motion of an object subject only to the acceleration due to gravity. (Note: the acceleration due to gravity is 9.8 m/s a. Find the velocity of the object for all relevant times. b. Find the position of the object for all relevant times. c. Find the time when the object reaches its highest point (What is the height?) d. Find the time when the object strikes the ground. A payload is released at an elevation of 500 m from a hot-air balloon that is rising at a rate of 14 m/s

Explanation / Answer

a) V = 14 - 9.8t

b ) S(t) = 14t - 4.9t^2 + 500

c ) v(t) = 0 ==> t = 1.42 sec

highest point = s (1.42 ) = 14(1.42) - 4.9(1.42)^2 + 500 = 510

d ) s(t) = 0 == > 510 - 4.9t^2 = 0 ==> t = 10.20 sec

total time = 10.20 + 1.42 =11.62 sec

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