Question #af942

1 Answer
Mar 13, 2017

Answer:

#t=3.6s#, rounded to one decimal place.

Explanation:

Using FPS system of units.

The kinematic expression is
#h(t)=h_0+ut+1/2g t^2#
Inserting given values and noting that acceleration due to gravity#32ft cdot s^-2# is acting against the direction of motion we get

#h(t)=7+54t+1/2(-32) t^2#
#h(t)=7+54t-16 t^2#
Which is the given equation.
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
We can start solution from here.

When the ball reaches ground #h=-7ft#
Inserting in the given height equation we get
#-7=7+54t-16 t^2#
#=>16 t^2-54t-14=0#
#=>8 t^2-27t-7=0#

Solving the quadratic with the inbuilt graphic tool we get two roots as below. Ignoring the #-ve# root as time can not be negative we get

my comp
#t=3.6s#, rounded to one decimal place.