Higher Derivatives Question

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NaazB_3.1415

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Hey I'm having trouble with this question:
"With what initial velocity must an object be thrown vertically upward in order to reach a man on a scaffold 15ft above?"
PS. I think this is a British calculus textbook so they use -32 ft/s^2 , instead of the -9.8m/s^2.
I tried solving this like this:
s(t) = -16t^2 + Vot (Vo is initial velocity)
V(t) = -32t + Vo
a(t) = -32
I reasoned that the initial velocity occurs when t=0, v(0) = Vo
and occurs when the displacement is equal to zero
0 = -16t^2 + Vot
0 = t(-16t + Vo), here I'm left with 2 unknowns so I don't know how to progress from here.
If I try to solve this from an algebraic physics perspective I get:
Vf^2 = Vo^2 + 2ad
0 = Vo^2 + 2(-32)(15)
960 = Vo^2
-31ft/s = Vo
I don't even know if this is correct because my book doesn't have the solution to this question.
Thanks
 
At maximal height, V(t)=0, therefore V0=32t. Now substitute this in your equation for s(t)=-16t2+V0t=15.
Can you proceed from here and solve? Why did you choose a negative value for V0? Your solution using the equation without time is almost right, just that you chose the wrong solution (negative).
 
Last edited:
yoscar04 said:
At maximal height, V(t)=0, therefore V0=32t. Now substitute this in your equation for s(t)=-16t2+V0t=15.
Can you proceed from here and solve? Why did you choose a negative value for V0? Your solution using the equation without time is almost right, just that you chose the wrong solution (negative).
Click to expand...
oH yeah I realized that after, I meant it to be positive, thanks
 
NaazB_3.1415 said:
Hey I'm having trouble with this question:
"With what initial velocity must an object be thrown vertically upward in order to reach a man on a scaffold 15ft above?"
PS. I think this is a British calculus textbook so they use -32 ft/s^2 , instead of the -9.8m/s^2.
I tried solving this like this:
s(t) = -16t^2 + Vot (Vo is initial velocity)
V(t) = -32t + Vo
a(t) = -32
I reasoned that the initial velocity occurs when t=0, v(0) = Vo
and occurs when the displacement is equal to zero
0 = -16t^2 + Vot
0 = t(-16t + Vo), here I'm left with 2 unknowns so I don't know how to progress from here.
If I try to solve this from an algebraic physics perspective I get:
Vf^2 = Vo^2 + 2ad
0 = Vo^2 + 2(-32)(15)
960 = Vo^2
-31ft/s = Vo
I don't even know if this is correct because my book doesn't have the solution to this question. Thanks
Click to expand...
NaazB_3.1415 said:
oH yeah I realized that after, I meant it to be positive, thanks
Click to expand...
England uses SI units of measurement not FPS. However, the given measurements are in ft - so FPS units are desired.

So you realized that the Vo must be positive (opposite direction compared to the gravitational force) - you should calculate it with at least 3 significant digits
 
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