Water fountain problem

did you make an attempt at this problem?

 

V in your equation is final velocity which should be zero. Vo is initial velocity which is what you are seeking. The sign on A is negative 9.8. And don't mix feet and meters.

 

the problem is asking for the *initial velocity*, which is v₀ in that formula

 

Nope, the initial velocity is not right. The water rises up to 150 ft. What does this tell you?

..and also, the given unit is ft. Then, g = 32 ft/s/s

 

when you throw something up into the air, there's a point at which it reaches its max height and then starts to come back down, yes? What's the velocity at the *instant* it reaches its maximum height?

 

Well, gravity drags the "projectile of the water" down. Consider throwing up the ball for example. If you toss the ball, then you exert the initial velocity v_0. At the highest point (or at the max height), the ball stops rising. That means v = 0 ft/s or v_f = 0 ft/s. After that time, the ball falls down due to gravity.

Following the example I have shown to you, find v_0.