An object is dropped from a balloon 3600 feet above the ground. Find the time it takes to reach
the ground if the height of the object is given by the equation h(t) = –16t^2 + 3600
it hits the ground when its height is zero, so just solve for t in
–16t^2 + 3600 = 0
plug in zero for h (the ground)
solve the quadratic for t
To find the time it takes for the object to reach the ground, we need to determine when the height of the object, represented by the equation h(t), becomes zero.
In this case, the equation for the height of the object is given by h(t) = -16t^2 + 3600, where t represents time in seconds.
Setting h(t) equal to zero, we have:
-16t^2 + 3600 = 0
To solve for t, we can start by factoring out a common factor of -16:
-16(t^2 - 225) = 0
Next, we can factor the quadratic equation t^2 - 225 using the difference of squares formula:
(t - 15)(t + 15) = 0
Now we have two possible solutions for t:
1) t - 15 = 0, which implies t = 15
2) t + 15 = 0, which implies t = -15
Since time cannot be negative in this context, we can disregard the solution t = -15.
Therefore, the only valid solution is t = 15.
Hence, it takes 15 seconds for the object to reach the ground.