How did i get this wrong? launching projectile

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In summary, the conversation discusses the launch of a block off a ramp with specific lengths and coefficients. The solution involves finding the velocity and distance at the end of the ramp, as well as the time it takes for the block to fall and the total time of the launch. The final answer was slightly off from the actual answer, leading to further discussion and investigation.
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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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Related to How did i get this wrong? launching projectile

1. How does the angle of launch affect the trajectory of a projectile?

The angle of launch is a crucial factor in determining the trajectory of a projectile. An object launched at a lower angle will have a shorter horizontal distance and a higher angle will result in a longer horizontal distance. This is because the vertical component of the initial velocity is affected by the angle of launch, while the horizontal component remains constant.

2. What role does air resistance play in the flight of a projectile?

Air resistance, also known as drag, can affect the flight of a projectile by slowing it down and altering its trajectory. The greater the surface area of the projectile, the more air resistance it will experience. This is why a flat object, like a sheet of paper, will fall more slowly than a spherical object with the same mass.

3. How does the mass of a projectile impact its flight?

The mass of a projectile affects its flight in two ways. First, a heavier projectile will be affected less by air resistance and will therefore have a longer range. Second, the greater the mass, the greater the force required to launch it, so a heavier projectile will require a stronger initial force to achieve the same velocity as a lighter projectile.

4. What is the relationship between the initial velocity and the range of a projectile?

The initial velocity of a projectile has a direct relationship with its range. This means that the higher the initial velocity, the greater the range will be. However, the angle of launch also plays a role, so a combination of a high initial velocity and an optimal angle of launch will result in the maximum range for a projectile.

5. How does changing the height of the launch affect the trajectory of a projectile?

The height of the launch will affect the trajectory of a projectile by changing the initial vertical velocity. A higher launch will result in a higher initial vertical velocity, causing the projectile to reach a higher peak height before falling. This will also result in a longer flight time and a longer horizontal distance traveled.

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