An object is thrown vertically from a height of #15 m# at # 19 m/s#. How long will it take for the object to hit the ground?

1 Answer
Feb 10, 2016

Answer:

#4.55 s#

Explanation:

The vertical distance the object travels is given by the equation
#y = v_(y0)t - 1/2g*t^2# where #v_(y0)# is the vertical component of the initial velocity, #g# is the acceleration due to gravity and #t# is the time taken to reach the highest point (where the velocity is zero).
The time can be found from the equation #v_(yf) = v_(yo) - g*t# by using the fact that #v_(yf) = 0#

Thus #0=19-9.8*t#
#t = 19/9.8 = 1.94 s#

The height the object reaches is therefore #19t - 9.8*t^2/2#
#=18.4 m#

We now have to work out how long the object will take to fall #18.4+15 = 33.4 m#

#33.4 =0*t + 1/2g*t^2#
#t = sqrt(33.4*2/9.8) =2.61 s#

The total time is #1.94 + 2.61 = 4.55 s#