A ball is thrown up with an initial velocity of 32 feet per second. How many seconds will it take for the ball to return to the ground using the formula h=vt-16t^2?

in h = 32t - 16t^2 , you are finding t when h = 0

32t - 16t^2 = 0
16t(2 - t) = 0
t = 0 or t = 2

it will take 2 seconds to return

(the t=0 gives you the initial height of 0)

Well, let's start by finding the time it takes for the ball to reach its highest point. The ball is thrown up, which means the initial velocity is positive. At the highest point, the velocity will be zero. So we can use the formula v = u + at and set v = 0 to solve for time.

0 = 32 - 32t

Simplifying this equation, we get:

32t = 32
t = 1

So it takes 1 second for the ball to reach its highest point.

Now, we need to find the time it takes for the ball to return to the ground. Since the ball is being thrown up, the total time for the ball to go up and come back down is twice the time it takes to reach the highest point.

Therefore, it will take 2 seconds for the ball to return to the ground.

But hey, don't take my word for it. Time flies like an arrow, and fruit flies like a banana.

To find the time it takes for the ball to return to the ground, we can set the height of the ball (h) equal to zero and solve for the time (t).

The given formula is h = vt - 16t^2, where:
h = height of the ball
v = initial velocity of the ball
t = time

Since the ball is thrown up, the initial velocity (v) will be positive (+32 feet per second).

Setting h to zero, we have:
0 = 32t - 16t^2

Rearranging the equation:
16t^2 - 32t = 0

Factoring out a common factor of 16t:
16t(t - 2) = 0

Now, we can set each factor equal to zero and solve for t:

First factor: 16t = 0
Dividing both sides by 16: t = 0

Second factor: t - 2 = 0
Adding 2 to both sides: t = 2

Therefore, the ball will take 2 seconds to return to the ground.

To find out how many seconds it will take for the ball to return to the ground, we can use the given formula h = vt - 16t^2.

First, let's assign the variables:
- h represents the height of the ball from the ground (we want to find when it becomes zero, as that indicates it has returned to the ground).
- v represents the initial velocity of the ball, which is given as 32 feet per second.
- t represents the time in seconds, which we need to determine.

We want to find the value of t when h = 0. So, we can set up the equation as follows:
0 = vt - 16t^2

Now, we can substitute the value of v into the equation:
0 = 32t - 16t^2

Next, we can rearrange the equation into a quadratic form:
16t^2 - 32t = 0

We can factor out the common factor of 16t:
16t(t - 2) = 0

Now, we set each factor equal to zero and solve for t:
16t = 0 OR t - 2 = 0

For the first factor:
16t = 0
Divide by 16:
t = 0

For the second factor:
t - 2 = 0
Add 2 to both sides:
t = 2

We have two possible values for t: t = 0 and t = 2. However, the ball has already been thrown up, so t = 0 does not make sense in this context. Thus, we consider t = 2 as the valid solution.

Therefore, it will take 2 seconds for the ball to return to the ground.