Find the time when velocity = 10 m/s

[tebes]

Homework Statement

v is the velocity.
v = (5.4t - 4.4t^2)i + 8.8 j
what is the time when v = 10 m/s

Homework Equations

The Attempt at a Solution

I tried the solution the following solution,
( (5.4t - 4.4t^2)^2 + 8.8^2 )^ 1/2 = 10
I solved for t.
But the highest power of t will be up to 4.
Is my method correct in solving the question above?

 

[LawrenceC]

Square the equation to get rid of the radical. Move the 8.8^2 to RHS leaving only something squared on LHS. Take square root and you are left with quadratic. The problem then is that the roots of the quadratic equation are imaginary. Are you sure you copied the problem correctly. B*B-4*A*C < 0.

 

[tebes]

Square the equation to get rid of the radical. Move the 8.8^2 to RHS leaving only something squared on LHS. Take square root and you are left with quadratic. The problem then is that the roots of the quadratic equation are imaginary. Are you sure you copied the problem correctly. B*B-4*A*C < 0.

yes. I double checked several times already. I was baffling with the same the problem too.
Therefore, i would get more then 1 positive answer, right ?

 

[LawrenceC]

No, you get the square root of a negative number for a time. Last time I looked, time was not an imaginary quantity. B*B-4*A*C is what is under the radical. If it is less than zero, then roots are imaginary.

 

[tebes]

No, you get the square root of a negative number for a time. Last time I looked, time was not an imaginary quantity. B*B-4*A*C is what is under the radical. If it is less than zero, then roots are imaginary.

Is it legit that I move the negative under the radical out ? I would get something like (xxx)^1/2 i ; i = -1. Am i correct ?

 

[LawrenceC]

Sure, you can remove the real part of the number.

(-9)^.5 = 3i where i is (-1)^.5

What bothers me is that the result is an imaginary number and how this relates to the phycality of the problem. If B were larger or if either A or C were different, you would not have a negative under the radical.