the height h in feet of a ball after t seconds is given by h=176t-16t^2. how long did it take to hit the ground
solve for t when h=0
56
To find out how long it took for the ball to hit the ground, we need to determine the value of t when the height h is equal to 0.
Given the equation: h = 176t - 16t^2
Setting h = 0, we have:
0 = 176t - 16t^2
Rearranging the equation, we get:
16t^2 = 176t
Dividing both sides by t, we have:
16t = 176
Now, dividing both sides by 16:
t = 11
Therefore, it took 11 seconds for the ball to hit the ground.
To find out how long it took for the ball to hit the ground, we need to determine when the height (h) equals zero. We can set up the equation as follows:
0 = 176t - 16t^2
To solve this quadratic equation, we can set it equal to zero and then factor or use the quadratic formula. Let's use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac))/(2a)
Comparing this formula with our equation, we have:
a = -16, b = 176, c = 0
Plugging these values into the quadratic formula:
t = (-(176) ± sqrt((176)^2 - 4(-16)(0)))/(2(-16))
Simplifying further:
t = (-176 ± sqrt(30976))/(-32)
Now, let's calculate the discriminant (b^2 - 4ac):
Discriminant = (176)^2 - 4(-16)(0) = 30976
Since the discriminant is positive, we will have two real solutions.
Substituting the discriminant back into the formula:
t = (-176 ± sqrt(30976))/(-32)
Now, calculate the square root of the discriminant:
sqrt(30976) = 176
Substituting this back into the formula:
t = (-176 ± 176)/(-32)
Now, we will calculate the two possible values of t:
t1 = (-176 + 176)/(-32) = 0/(-32) = 0
t2 = (-176 - 176)/(-32) = -352/(-32) = 11
Since we are considering time (t), a negative value is not meaningful in this context. Therefore, the ball hit the ground after 11 seconds.