Thread: Applications for Derivatives (velocity)

*insert long descriptive paragraph about a volcano*
Paraphrase: With regards to a shot of lava at a point 1900 ft shooting straight into the air, what was the lava's exit velocity in feet per second? in miles per hour?

[HInt: If v0 is the exit velocity of a particle of lava, its height t seconds later will be s= v0t - 16t^2 feet. Begin by finding the time at which ds/dt= 0. Neglect air resistance]

I assume v0 is just another term for the first velocity.

ds/dt= v0 - 32t

v0 - 32t = 0

v0 = 32t

That seems unhelpful.

What now? or did I misunderstand?


Thanks!

Hello, Truthbetold!

With regards to a shot of lava at a point 1900 ft shooting straight into the air,
what was the lava's exit velocity in feet per second? in miles per hour?

Hint: If is the exit velocity of a particle of lava,
its height seconds later will be: . feet.
Begin by finding the time at which

I assume is just another term for the first velocity. . . . . Yes!


. . . You were well on your way . . .

You found that the lava reached maximum height at: . seconds.

Then the maximum height is: . feet


But we are told that the maximum height is 1900 feet.

. . So we have: .

Got it?