The height h in feet reached by a golf ball after t seconds is given by h(t)=-16t squared+120t, After how many seconds does the golf ball strike the ground?
-16t^2 + 120t = 0
Use Quadratic Formula and get:
Tr = 3.75 s. = Rise time or time to reach max ht.
Tf = Tr = 3.75 s. = Fall time.
T = Tr + Tf = 3.75 + 3.75 = 7.50 s. To
strike gnd.
To find the time at which the golf ball strikes the ground, we need to determine when the height of the ball is zero (h(t) = 0).
In this case, we have the equation h(t) = -16t^2 + 120t.
To solve for t, we set the equation equal to zero:
-16t^2 + 120t = 0
To make the equation easier to solve, we can factor out common terms:
-16t(t - 7.5) = 0
Now we have two factors. Either -16t = 0 or (t - 7.5) = 0.
Solving -16t = 0 gives us t = 0.
Solving (t - 7.5) = 0 gives us t = 7.5.
Therefore, the golf ball strikes the ground after 7.5 seconds.