Question

Constants Periodic Table PartA A skateboarder starts up a 1.0-m-high, 30° ramp at a speed of 5.5 m/s. The skateboard wheels roll without friction. At the top, she leaves the ramp and sails through the air. How far from the end of the ramp does the skateboarder touch down? Express your answer to two significant figures and include the appropriate units value Units t=

Answer 1

Part -A

Solve this problem using conservation of energy.

According to conservation of energy -

Initial KE = Final KE + Final PE

which after dividing through by mass/2 gives

Vi² = Vf² + 2gh

Put the values -

(5.5 m/s)² = Vf² + 2*9.8m/s²*1m

=> Vf² = 30.25 - 19.6 = 10.65

=> Vf = 3.26 m/s

Now we have the launch velocity, and we know the launch angle = 30º

Vertically, Vy = Vf*sinΘ = 3.26 m/s * sin30º = 1.63 m/s

Now use the expression -

s = So + Vy*t + ½at²

=> 0 = 1m + 1.63m/s*t - 4.9m/s²*t²

Write in simpler form -

4.9t^2 - 1.63t - 1 = 0

So -

t = [1.63 + sqrt(1.63^2 + 4*4.9*1)] / (2*4.9) = [1.63 + 4.72] / 9.8 = 0.65 s

Other value of t is discarded because it is negative.

So, t = 0.65 s ← time of flight

Then horizontally we have

x = Vx*t = Vf*cosΘ*t = 3.26 m/s * cos30º * 0.65s = 1.84 m

Answer in two significant digits is -

l = 1.80 meter.