The formula h=48t-16t^2 gives the height, h, in feet, of an object projected into the air after t seconds. If an object is propelled upward, at what time(s) will it reach a height of 32 feet above the ground?
To find the time(s) when the object reaches a height of 32 feet above the ground, we need to substitute h = 32 into the formula h = 48t - 16t^2 and solve for t.
So, we have 32 = 48t - 16t^2.
Let's rearrange the equation to solve for t:
16t^2 - 48t + 32 = 0
Dividing the equation by 16, we get:
t^2 - 3t + 2 = 0
Now, let's factor the quadratic equation:
(t - 1)(t - 2) = 0
Setting each factor equal to zero, we have:
t - 1 = 0 or t - 2 = 0
Solving these equations, we find:
t = 1 or t = 2
Therefore, the object will reach a height of 32 feet at t = 1 second and t = 2 seconds.
To find the time(s) at which the object reaches a height of 32 feet, we need to solve the equation h = 32 for t using the given formula h = 48t - 16t^2.
1. Start with the equation h = 48t - 16t^2.
2. Replace h with 32, since we want to find the time(s) when the object reaches a height of 32 feet: 32 = 48t - 16t^2.
3. Rearrange the equation by moving all terms to one side to form a quadratic equation: -16t^2 + 48t - 32 = 0.
4. Divide the entire equation by -16 to simplify: t^2 - 3t + 2 = 0.
5. Factor the quadratic equation: (t - 1)(t - 2) = 0.
6. Set each factor equal to zero and solve for t:
t - 1 = 0, which gives t = 1.
t - 2 = 0, which gives t = 2.
Therefore, the object will reach a height of 32 feet at t = 1 second and t = 2 seconds.
h = 48t - 16t^2 = 32 Ft.
Divide both sides by 16:
3t - t^2 = 2,
-t^2 + 3t - 2 = 0.
Solve using the Quadratic Eq and get:
t = 1s, and t = 2s.