A stone is dropped from a helicopter which is rising steadily at #19.6ms^-1#. If the stone is released when the helicopter is at an altitude of #24.5m#, how long does it take for the stone to reach the ground?

1 Answer
MattyMatty
Feb 5, 2018

#"5 seconds"#

Explanation:

#h = h_0 + v_0*t - g*t^2/2#

#h_0 = 24.5#
#v_0 = 19.6#
#g = 9.8#
#h = 0 " (when stone reaches the ground h=0)"#

#=> 0 = 24.5 + 19.6*t - 4.9*t^2#

#=> 4.9*t^2 - 19.6*t - 24.5 = 0#
#"This is a quadratic equation with discriminant :"#
#19.6^2 + 4*4.9*24.5 = 864.36 = 29.4^2#
#=> t = (19.6 pm 29.4)/9.8#
#"As time is positive, we must take the solution with + sign : "#
#=> t = 49/9.8 = 5#

#h_0 = " initial height in meter (m)"#
#h = " height in meter (m)"#
#v_0 = " initial velocity in m/s"#
#g = " gravity constant = "9.8 "m/s²"#
#t = " time in seconds (s)"#

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