if an object is projected upward from ground level with an initial velocity of 64 ft per sec,its height h in feet t seconds later is h=-16t+64t.after how many seconds is the height 48 ft.
48= -16t+64t^2
put it in quadratic form:
4t^2-t-3=0
(2t-3)(2t+1)=0
so t= 3/2 second, disregard the negative answer
Well, let's solve this mathematical problem with a touch of humor, shall we?
To find out after how many seconds the height is 48 feet, we can substitute the value of h into the equation and solve for t:
48 = -16t + 64t
Now, let's combine like terms:
48 = 48t
Now, let's divide both sides by 48:
t = 1
Voilà! After just one second, the object reaches a height of 48 feet. Which goes to show that success can sometimes come quickly, just like the punchline of a good joke!
To find the time it takes for the object to reach a height of 48 ft, we can set the equation for height equal to 48 ft and solve for t.
Given equation: h = -16t + 64t
Setting h = 48 ft: 48 = -16t + 64t
Simplifying the equation: 48 = 48t
Dividing both sides by 48: t = 1
Therefore, the height of 48 ft is reached after 1 second.
To find out after how many seconds the height is 48 ft, we can set the equation h = 48 and solve for t.
Given the equation: h = -16t^2 + 64t
We substitute h with 48: 48 = -16t^2 + 64t
Rearranging the equation to set it equal to zero: -16t^2 + 64t - 48 = 0
This is now a quadratic equation in the form of at^2 + bt + c = 0, where a = -16, b = 64, and c = -48.
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values, we get: t = ( -64 ± √(64^2 - 4(-16)(-48)) ) / 2(-16)
Simplifying further: t = ( -64 ± √(4096 - 3072) ) / -32
Calculating inside the square root: t = ( -64 ± √1024 ) / -32
Taking the square root: t = ( -64 ± 32 ) / -32
We have two possibilities:
1) t = (-64 + 32) / -32 = -32 / -32 = 1
2) t = (-64 - 32) / -32 = -96 / -32 = 3
Therefore, the height of 48 ft is reached after 1 second and 3 seconds.