How Far Does a Skateboarder Land from a Ramp?

[ideefixem]

Homework Statement

A skateboarder starts up a 1.0 m high 30 degree ramp at a speed of 7.0 m/s. The skateboard wheels roll without friction. How far from the end of the ramp does the skateboarder touch down?

The Attempt at a Solution

ramp length=
h=1sin30=1/2
length=2m

v^2=vi^2+2ad
v^2=7^2+2(-9.8)(2)
vf=3.13m/s

vf=vi+a(Dt)
0=3.13+-9.8(t)
delta t=.32s

Xf=xi+vi(dT)
x=0+3.13(.32)
xf=1.0016

yf=yi+vi(dt)+1/2a*(dt)^2
yf=1+0(.32)+1/2(-9.8)(.32)^2
yf=0

The skateboarder lands 1.0016 meters from the end of the ramp.




I know I'm missing something somewhere... can someone please help me find it.

 

[ideefixem]

Hmm... That wasn't even close... Let me try this again.

cos30(7)=vx= 6.06 m/s
sin30(7)=vy= 3.5 m/s

-1=3.5(t)+.5(-9.8)(t^2)
0=-4.9t^2+3.5t+1
t= 0.933 s

x= (6.06)(.933)+.5(0)(.933)^2
x= 5.65 m

How does that look?

 

[ogb p]

Your calculations seem to be correct based on the given information. However, it is important to note that these calculations assume ideal conditions, such as a perfectly smooth ramp and no air resistance. In reality, there may be other factors that could affect the distance the skateboarder travels, such as wind resistance and the surface of the ramp. Additionally, the skateboarder's technique and body position could also play a role in the distance they travel. As a scientist, it is important to consider all possible variables and limitations when making calculations and drawing conclusions.