A model rocket is launched with an initial upward velocity of 65 m/s. The rocket's height h (in meters) after t seconds is given by the following.
h = 65t-5t^2
Find all values of t for which the rocket's height is 25 meters:
To find the values of t for which the rocket's height is 25 meters, we need to set h equal to 25 and solve for t.
25 = 65t - 5t^2
Rearranging the equation, we get:
5t^2 - 65t + 25 = 0
Now, we can solve this quadratic equation using the quadratic formula:
t = (-(-65) ± √((-65)^2 - 4*5*25))/(2*5)
t = (65 ± √(4225 - 500))/10
t = (65 ± √3725)/10
t = (65 ± √3725)/10
t = (65 + 61.1)/10 or t = (65 - 61.1)/10
t = 126.1/10 or t = 3.9/10
t = 12.61 or t = 0.39
Therefore, the rocket's height is 25 meters at t = 0.39 seconds and t = 12.61 seconds.