Question

The skateboarder in the drawing starts down the left side of the ramp with an initial speed of 5.4 m/s. Neglect nonconservative forces, such as friction and air resistance, and find the height h of the highest point reached by the skateboarder on the right side of the ramp.

Answer 1

Answer:

1.5 m

Explanation:

Using the law of conservation of energy

Gain in potential energy by the skateboarder=  Loss in kinetic energy by the skateboarder

PE=KE where KE represent potential energy, PE represent potential energy

$KE=0.5mv^{2}$ where m is mass of skateboarder and v is velocity of skateboarder

PE=mgh where m is the mass of skateboarder, g is acceleration due to gravity which in this case is taken as $9.81 m/s^{2}$ and h is the highest point reached by the skateboarder. Equating PE=KE we have

$mgh=0.5mv^{2}$ and since m are on both LHS and LHS, the cancel

$gh=0.5v^{2$} and making h the subject of the above formula

$h=\frac {0.5v^{2}}{g}$

Substituting v with 5.4 m/s and g as $9.81 m/s^{2}$ we obtain

$h=\frac {0.5*(5.4 m/s)^{2}}{9.81}=1.486238532 m$

Rounded off, h=1.5 m