If an object is propelled upward fom a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation he=−16t squared + vt + s, where h is in feet. If the object is propelled from a height of 44 feet with an initial velocity of 64 feet per second, its height h is given by the equation h=−16t squared + 64t + 4.

Question

If an object is propelled upward fom a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation he=−16t squared + vt + s, where h is in feet. If the object is propelled from a height of 44 feet with an initial velocity of 64 feet per second, its height h is given by the equation h=−16t squared + 64t + 4.

After how many seconds is the height 64feet?

Answer 1

S = 44; Not 4.

h = -16t^2 + 64t + 44 = 64.
Divide both sides by 4:
-4t^2 + 16t + 11 = 16,
-4t^2 + 16t -5t = 0,
Use Quadratic Formula:
t = {-16 +- Sqrt(256-80))/-8,
t = (-16 +- 13.3)/-8 = 0.342, and 3.66 Seconds. t = 3.66 seconds.

Answer 2

To find the number of seconds when the height is 64 feet, we need to solve the equation h = -16t^2 + 64t + 4 for h = 64.

Substituting h = 64 into the equation, we get:

64 = -16t^2 + 64t + 4

Rearranging the equation, we have:

16t^2 - 64t + 60 = 0

Now we can solve this quadratic equation to find the value of t. There are several methods to solve this equation, such as factoring, completing the square, or using the quadratic formula.

In this case, let's use factoring:

16t^2 - 64t + 60 = 0

Divide through by 4 to simplify the equation:

4t^2 - 16t + 15 = 0

Now let's look for two numbers that multiply to give 15 and add up to -16. Those numbers are -1 and -15:

(4t - 1)(t - 15) = 0

Setting each factor equal to zero:

4t - 1 = 0 or t - 15 = 0

Solving each equation separately:

4t = 1 or t = 15

t = 1/4 or t = 15

Since we are considering time, the negative value of t is not valid. Thus, the object's height will be 64 feet after 15 seconds.