Please answer both parts and show steps. 1. Consider the following description o

Question

Please answer both parts and show steps.

1. Consider the following description of the vertical motion of an object subject only to the acceleration due to gravity. Begin with the acceleration equation a(t) = v(t) = 9.8 m/s2. A stone is thrown vertically upward with a velocity of 30 m/s from the edge of a cliff 200 m above a river.

(a) Find the velocity of the object at all relevant times (that is, find the velocity function).

(b) Find the position of the object for all relevent times (that is, find the position function).

Explanation / Answer

a)

a(t) = v(t) = 9.8 m/s2

v(t)=integral v(t) dt = 9.8t +c

initially velocity v(0)=30m/s

9.8*0+c =30

==>c=30

v(t)= 9.8t +30

b)position s(t)=integral v(t) dt

s(t)= 9.8t2/2 +30t +c

s(t)= 4.9t2 +30t +c

initially stone is 200 m above a river

s(0)=200m

s(0)= 4.9*02 +30*0 +c=200

==>c=200

position s(t)=4.9t2 +30t +200

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