The height h(t), in feet, of an airborne tee-shirt t seconds after begin launch can be approximated by h(t)= -15t^2+120t+10,0<t<10.
Find the times when the tee shirt will reach a fan 190 feet above ground level
To find the times when the tee-shirt will reach a fan 190 feet above ground level, we need to solve the equation h(t) = 190.
Given that h(t) = -15t^2 + 120t + 10, we substitute 190 for h(t):
-15t^2 + 120t + 10 = 190
Rearranging the equation, we get:
-15t^2 + 120t + 10 - 190 = 0
Simplifying further:
-15t^2 + 120t - 180 = 0
Divide through by -15 to simplify the equation:
t^2 - 8t + 12 = 0
Factor the quadratic equation:
(t - 2)(t - 6) = 0
Setting each factor equal to zero:
t - 2 = 0 or t - 6 = 0
Solve for t:
t = 2 or t = 6
Therefore, the tee-shirt will reach a fan 190 feet above ground level at t = 2 seconds and t = 6 seconds.
To find the times when the tee shirt will reach a fan 190 feet above ground level, we need to set up the equation and solve for t in the given function.
The equation for the height of the tee shirt can be written as h(t) = -15t^2 + 120t + 10.
We want to find the times when the height, h(t), is equal to 190 feet. Setting h(t) = 190, we have:
-15t^2 + 120t + 10 = 190
Now, let's rearrange the equation to have a quadratic equation where one side is equal to zero:
-15t^2 + 120t - 180 = 0
Dividing the entire equation by -15 to simplify, we get:
t^2 - 8t + 12 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. To solve it using factoring, we need to find two numbers that multiply to give 12 and add to give -8. The numbers are -6 and -2:
(t - 6)(t - 2) = 0
Setting each factor equal to zero, we get:
t - 6 = 0 or t - 2 = 0
Solving for t, we have:
t = 6 or t = 2
So, the tee shirt will reach a fan 190 feet above ground level at t = 6 seconds and t = 2 seconds.