A model rocket is launched upward with an initial velocity of 220 feet per second. The height, in feet, of the rocket t seconds after the launch is given by the function: h(t) = -16t^2 + 220t .
How many seconds after launching the rocket will the rocket be 350 feet above the ground?
I really appreciate any help in this..
How many seconds after launching the rocket will the rocket be 350 feet above the ground?
I really appreciate any help in this..
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The position function is given: h(t) = -16t^2 +220t and h(t) represents the position.
Therefore, you can set the position function equal to the number of feet above the ground it is: 350ft
You get: -16t^2 + 220t = 350 and from there just subtract the 350 over to the other side and solve for t by factoring 16t^2 - 220t + 350 = 0 (multiplied by -1 to make it easier)
You'll get to positive values of t and I believe you'll want to use the smaller one as it would be the first time to reach 350ft. The reason for two values of t is because 350ft isn't where the rocket maxes out so there is a point on the way up that reaches 350ft and a point when the rocket is falling that it reaches 350ft and the function is a negative quadratic if that helps as well and it in fact maxes at 406.25 fyi :D
Therefore, you can set the position function equal to the number of feet above the ground it is: 350ft
You get: -16t^2 + 220t = 350 and from there just subtract the 350 over to the other side and solve for t by factoring 16t^2 - 220t + 350 = 0 (multiplied by -1 to make it easier)
You'll get to positive values of t and I believe you'll want to use the smaller one as it would be the first time to reach 350ft. The reason for two values of t is because 350ft isn't where the rocket maxes out so there is a point on the way up that reaches 350ft and a point when the rocket is falling that it reaches 350ft and the function is a negative quadratic if that helps as well and it in fact maxes at 406.25 fyi :D