How would I use the kinematic equations to derive a general equation for the time it takes a ball dropped from rest at vertical height #h# to reach the ground?

I'm pretty sure that the answer would be
(1) #t = sqrt((2h)/(g))#
(2) Use the result from the part (1) above to write a general equation for the distance travelled by a projectile that is rolling off a table of height #h# with a horizontal speed, #v_(0x)#.

1 Answer
A08
Jun 22, 2017

The kinematic expression is

#s=ut+1/2 a t^2#

For a free falling body from height #h# under action of gravity #g# and starting from rest above expression becomes

#h=0xxt+1/2 g t^2#

Solving for #t# we get

# t^2=(2h)/g#
# t=sqrt((2h)/g)#
(2) Horizontal speed #=v_(0x)#
Horizontal distance # s# traveled in time #t#
#s="velocity"xx"time"#
#s=v_(0x)xxsqrt((2h)/g)#

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