How Do I Solve This Kinematic Equation Problem with Gravity?

[riseofphoenix]

So I'm given...

In the y-direction
v_o = 0 m/s
v_f = 7.5 m/s (is the speed of the ball thrown straight up)
g = -9.81 m/s² (when it falls back down)

y_o = 0 m
y_f = 1.5 m (at this height above the ground, the bat connects with the ball)

t = ?

I tried doing this...

y_f = y_o + v_yot + (1/2)gt²
1.5 = 0 + (0)t + (1/2)(-9.81)t
1.5 = -4.905t
0.30581 = t

:(
Help?

 

[TSny]

So I'm given...

In the y-direction
v_o = 0 m/s
v_f = 7.5 m/s (is the speed of the ball thrown straight up)

Projectile motion starts just after the ball leaves the bat. So, the initial velocity is not zero. The final velocity would be the velocity the ball strikes the ground (not given).

Similarly, think about the initial and final values of y.

 

[riseofphoenix]

Projectile motion starts just after the ball leaves the bat. So, the initial velocity is not zero. The final velocity would be the velocity the ball strikes the ground (unknown).

Similarly, think about the initial and final values of y.

Ok... So

v_o = 7.5 m/s (initial speed of the ball when thrown straight up)
v_f = ____ m/s (the final speed when the ball strikes the ground)
g = -9.81 m/s² (when it falls back down)

y_o = 1.5 m
y_f = 0 m (at this height above the ground, the bat connects with the ball)

t = ?

Like that?

 

[TSny]

Yes. Good.

 

[riseofphoenix]

Yes. Good.

y_f = y_o + v_yot + (1/2)gt²

0 = 1.5 + 7.5t + (1/2)(-9.81)t²
0 = 1.5 + 7.5t - 4.095t²
0 = - 4.095t² + 7.5t + 1.5

Quadratic formula:

[ -b ± √(b² - 4ac) ] / 2a
= [ -7.5 ± √(7.5² - 4(-4.095)(1.5)) ] / 2(-4.095)
= [ -7.5 ± √(56.25 +24.57) ] / -8.19
= [ -7.5 ± √(80.82) ] / -8.19
= ( -7.5 ± 8.989 ) / -8.19
= ( -7.5 - 8.989 ) / -8.19
= -16.48999444 / -8.19
= -16.48999444 / -8.19
t = 2.013 s


What did I do wrong??

 

[TSny]

Looks like just a slip. Half of 9.81 is not 4.095

 

[riseofphoenix]

Looks like just a slip. Half of 9.81 is not 4.095

Oh yeah...i just realized that..the answer is supposed to be A :)

Can you help me out with one more?

I tried doing...
a² + b² = c² after making my triangle...

3.2² + b² = 12²
b² = 144-10.24
b = √(133.76)
b = 11.56

And then I tried doing

12*sin (18.9) = 3.89 m

 

[haruspex]

Don't you think gravity might come into it somewhere?