A student is skateboarding down a ramp that is 8.33 m long and inclined at 24.5° with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 4.12 m/s. Neglect friction and find the speed at the bottom of the ramp.
h = L*sin A = 8.33*sin 24.5 = 3.45 m.
V^2 = Vo^2 + 2g*h
V^2 = 4.12^2 + 19.6*3.45 =
Solve for V.
To find the speed of the skateboarder at the bottom of the ramp, we can use the principle of conservation of energy. At the top of the ramp, the skateboarder has potential energy due to height and kinetic energy due to motion. At the bottom of the ramp, all the potential energy is converted to kinetic energy.
The potential energy at the top of the ramp can be calculated using the formula:
PE = m * g * h
Where PE is the potential energy, m is the mass of the skateboarder, g is the acceleration due to gravity and h is the height of the ramp.
The kinetic energy at the bottom of the ramp can be calculated using the formula:
KE = 0.5 * m * v^2
Where KE is the kinetic energy and v is the velocity of the skateboarder at the bottom of the ramp.
Since energy is conserved, the potential energy at the top of the ramp is equal to the kinetic energy at the bottom of the ramp:
PE = KE
Plugging in the values:
m * g * h = 0.5 * m * v^2
The mass of the skateboarder cancels out:
g * h = 0.5 * v^2
Now we can solve for v by rearranging the equation:
v^2 = (2 * g * h)
Taking the square root of both sides:
v = sqrt(2 * g * h)
Given that g is approximately 9.8 m/s^2 and h is the height of the ramp, we can calculate the height of the ramp using trigonometry.
h = l * sin(angle)
Where l is the length of the ramp and angle is the angle of inclination.
Plug in the given values:
h = 8.33 m * sin(24.5°)
Now we can substitute the value of h into the equation to find v:
v = sqrt(2 * 9.8 m/s^2 * 8.33 m * sin(24.5°))
Calculating v:
v ≈ sqrt(2 * 9.8 * 8.33 * 0.406)
v ≈ sqrt(65.41)
v ≈ 8.1 m/s
Therefore, the speed of the skateboarder at the bottom of the ramp is approximately 8.1 m/s.