The height, measured in meters (m), of a falling object as a function of time, measured in seconds(s)?

Question

is given by a function h=f(t). Using units, explain the meaning of the following statements:

a) h(2)=6
b) h'(2)= -17

Answer 1

h=-1/2g*t^2 +Vot +ho
at t= 2s
6= -2g +2Vo+ho
h´(t)=- gt+Vo
h´(2)= -2g+Vo=-17so Vo= 2.6 m/s upwards
ho=m
so h(t) = -1/2gt^2 +2.6t +20.40 (h in m ,t in s)

Answer 2

(a) After two seconds, the height is 6 m.

(b) h' is the first derivative of the height function, which gives the object's velocity. Hence after two seconds, the velocity is 17 m/s in a downward direction.

Answer 3

h=a.t2
where a is the gravity acceleration equals 9.81 m/s2