The upward velocity of the water in the stream of a particular fountain is given by the formula v = -32t + 28, where t is the number of secondds after the water leaves the fountain. While going upward, the water slows down until, at the top of the stream, the water has a velocity of 0 feet per second. How long does it take a droplet of water to reach the maximum height?

t= number of seconds after water leaves the fountain

v=-32t+28 where v=0
So, 0=-32t+28
32t=28
t=28/32
t=0.875

If v=0

0=-32t+28
solve for t.

To find out the time it takes for the droplet of water to reach the maximum height in the fountain, we need to find the value of t when the velocity v is 0.

Given that the formula for the velocity v is v = -32t + 28, we set v to 0 and solve for t:

0 = -32t + 28

To isolate t, we can move 28 to the other side of the equation:

32t = 28

Now, divide both sides of the equation by 32:

t = 28 / 32

Simplifying:

t = 7/8

Therefore, it takes a droplet of water 7/8 seconds to reach the maximum height in the fountain.

To find out how long it takes a droplet of water to reach the maximum height, we need to determine the value of 't' when the velocity of the water reaches 0 feet per second.

Given that the formula for the velocity is v = -32t + 28, we set v = 0:
0 = -32t + 28

To solve this equation for 't', we can add 32t to both sides of the equation:
32t = 28

Next, we isolate 't' by subtracting 28 from both sides of the equation:
32t - 28 = 0

Finally, we divide both sides of the equation by 32:
t = 28/32

Simplifying, we get:
t = 7/8

Therefore, it takes a droplet of water 7/8 of a second to reach the maximum height.