Consider the following descriptions of the vertical motion of an object subject
ID: 1449761 • Letter: C
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^2)
A payload is released at an elevation of 700m from a hot-air balloon that is rising at a rate of 13 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
Explanation / Answer
a)
The velocity of the object for all relevant times is
v =13-9.8*t
b)
The position of the object is
s =13*t -4.9*t2
c)
We know that at the heighest point final velocity is zero (v=0)
t =13m/s/9.8 =1.326s
s =13*1.326-4.9*(1.326)2 =17.238-8.622=8.616m
Therefore heighestpoint H =700+8.616 =708.616
d)
The time when the object strikes the ground is given by
s(t) = 0 == > 708.616 - 4.9t^2 = 0
t = 12.025 sec
total time = 12.025 + 1.326 = 13.351 sec