A ball is tossed vertically upwards with a speed of 5.0 m s–1. After how many seconds will the ball return to its initial position?

The answer is 1 second. I keep getting 0.5 s I used v=u+at

1 Answer
A08
Apr 28, 2018

Applicable kinematic expression is

#h=ut+1/2g t^2#

Note that acceleration due to gravity #g=9.81ms^-2# acts in a direction opposite to initial direction of motion.
When ball returns to initial position its height #h=0#. Inserting given values we get

#0=5t+1/2(-9.81)t^2#
#=>9.81t^2-10t=0#
#=>t(9.81t-10)=0#

Roots of this quadratic are
#t=0#, corresponds to the initial position.
and #t=10/9.81=1.01\ s#, rounded to two decimal places

.-.-.-.-.-.-.-.-

If you want to use

#v=u+at#

Note that final velocity is in a direction opposite to initial velocity. Hence, #u=5.0\ ms^-1 and v=-5\ ms^-1#, #a=-g#
Of course if you can use #g=10\ ms^-2# to get desired answer.

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