How did i get this wrong? launching projectile

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SUMMARY

The discussion focuses on the calculation of the projectile motion of a block launched from a ramp with a length of 5 meters and a kinetic coefficient of 0.2. The initial velocity of the block is 12 m/s, leading to a calculated velocity at the end of the ramp of 8.47 m/s, which aligns with the answer sheets. However, the total horizontal distance calculated is 10.9 meters, while the expected answer is 9.78 meters. The discrepancy arises from the incorrect application of the equations of motion and the effects of friction on the block's trajectory.

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Homework Statement



A block is being launch of a ramp, the length of the ramp is 5m(hypotenuse). The ramp also has a kinetic coefficient of .2 and the block has an initial velocity of 12m/s.


Homework Equations



-Wx-uFn = ma

Velocity equations for finding distance off the ramp

The Attempt at a Solution



ok to find the velocity at the end of the ramp.

-mgsin35-umgcos(35) = ma
15.6 - 1.6 = -7.2 s

V^2 + Vi^2 + 2at(change in x)
V= Square root(12^2 + 2(-7.2)(5))
V at the end of the ramp is 8.47 ms (this was confirm right by the answer sheets)

finding the velocity in all direction

Vy = 4.86 ms
Vx = 6.94 ms
V = 8.47 ms

now for the distance, I am going to find the time it takes for Vy to reach zero

Vyf = Vyi +at
0 = 4.8 + (-9.8)t
t=.49

time it takes for it to fall down
Height of the ramp 2.87
Height of the pojectable when Vy = 0 2.384
total height 5.25

0= 5.25 + 1/2(-9.8)t
T= 1.07s

Total time = 1.57s

x=0+6.94(1.57) = 10.9m

but the actual answer is 9.78

why am i off?
 
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