A skate boarder starts down the left side of a ramp with an initial speed of 5.4 m/s. Ignoring any non-conservative forces such as friction and air resistance, what would be the height h of the highest point reached by the skateboarder when she is launched from the right side of the ramp?
1.49m
To solve this problem, we can make use of the conservation of mechanical energy. The skateboarder starts with an initial kinetic energy (KE) due to her velocity, and this energy will transform into potential energy (PE) as she gains height.
The total mechanical energy (E) remains constant throughout the entire motion, since we're ignoring non-conservative forces like friction and air resistance. So, we can equate the initial KE to the final PE at the highest point.
The initial kinetic energy is given by:
KE = (1/2)mv²
Where:
m = mass of the skateboarder
v = initial velocity = 5.4 m/s
Since the mass of the skateboarder is not given, we can assume it cancels out when solving for the height, so we won't include it in the calculation.
The final potential energy at the highest point is given by:
PE = mgh
Where:
g = acceleration due to gravity = 9.8 m/s²
h = height
Setting the initial KE equal to the final PE, we have:
(1/2)mv² = mgh
Canceling out the mass and rearranging the equation gives us:
v² = 2gh
Solving for h gives us:
h = (v²) / (2g)
Now we can substitute the given values into the equation to find the height:
h = (5.4 m/s)² / (2 * 9.8 m/s²)
h = 2.43 m
Therefore, the height reached by the skateboarder when she is launched from the right side of the ramp is approximately 2.43 meters.