The Formula H=VoT-16t^2 gives the height (h) in feet of an object after t seconds. Here, Vo is the initial velocity of the object expressed in feet per second. Supposed a toy rocket was launched from the ground straight up with an initial velocity of 112 ft/sec. How many seconds after launch was the rocket 160 feet above the ground?
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Assuming you meant: H = Vo*t - 16t^2
With the given information it becomes: H = 112t - 16t^2
Setting this equal to the required height:
160 = 112t - 16t^2
16t^2 - 112t + 160 = 0
16(t^2 - 7t + 10) = 0
16*(t - 2)(t - 5) = 0
t = 2, 5 seconds. Once on the way up and once again on the way down.
With the given information it becomes: H = 112t - 16t^2
Setting this equal to the required height:
160 = 112t - 16t^2
16t^2 - 112t + 160 = 0
16(t^2 - 7t + 10) = 0
16*(t - 2)(t - 5) = 0
t = 2, 5 seconds. Once on the way up and once again on the way down.