A model rocket is launched from a height of 50 feet. the formula: h=-16t^2+70t+50 describes the rocket's height,h,in feet t seconds after it was launched. how long will it take the rocket to reach the ground.
when it hits the ground, h = 0
-16t^2 + 70t + 50 = 0
8t^2 - 35t - 25 = 0
(t-5)(8t + 5) = 0
t = 5 or t = -5/8, but t can't be negative
so it will hit the ground in 5 seconds.
To find out how long it takes for the rocket to reach the ground, we need to determine the time when the height (h) is equal to zero. In this case, the height of the rocket is given by the equation h = -16t^2 + 70t + 50, where h represents the height in feet and t represents the time in seconds.
To solve for t, we can set the equation equal to zero:
-16t^2 + 70t + 50 = 0
Now, we can use the quadratic formula to solve for t. The quadratic formula is given by:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -16, b = 70, and c = 50. Plugging these values into the formula, we get:
t = (-70 ± √(70^2 - 4(-16)(50))) / (2(-16))
Simplifying this equation gives us:
t = (-70 ± √(4900 + 3200)) / (-32)
t = (-70 ± √8100) / (-32)
Now, calculating the square root of 8100, we get:
t = (-70 ± 90) / (-32)
This gives us two possible values for t:
t = (-70 + 90) / (-32) = 20 / (-32) = -0.625
t = (-70 - 90) / (-32) = -160 / (-32) = 5
Since time cannot be negative, we discard the negative value of t. Therefore, the rocket will reach the ground after approximately 5 seconds.