Projectile Motion: Finding Time to Change Angle from 31° to 21°

[randomguy123]

Homework Statement

In the javelin throw at a track-and-field event, the javelin is launched at a speed of 23 m/s at an angle of 31° above the horizontal. As the javelin travels upward, its velocity points above the horizontal at an angle that decreases as time passes. How much time is required for the angle to be reduced from 31° at launch to 21°?

Homework Equations

velocity & time:
v = v0 + a * t

The Attempt at a Solution

First I found the horizontal and vertical velocities when the angle is 31°:

Vx1 = cos(31) * 23 = 19.7
Vy1 = sin(31) * 23 = 11.8

Then I found the horizontal and vertical velocities when the angle is 21°:

Vx2 = Vx1 = cos(31) * 23 = 19.7
Vy2 = Vy1 + (-9.8) * t

Lastly, in order to find t:

tan(21) = Vy2 / Vx2 = ( 11.8 - 9.8 * t ) / 19.7

t ~= .44 seconds

Apparently, this is not the right answer
Please let me know what I am doing wrong. Thank you !

 

[H_man]

Your working looks fine to me... what is the stated answer? Perhaps there is an error in the textbook?

 

[randomguy123]

Unfortunately I'm using WebAssign and all it tells me is if the answer is correct or incorrect.