1. A skateboarder coasts at a constant velocity toward a ramp with a 15 angle, preparing for the big trick jump. If the frictionless ramp is 3m long, and his initial velocity at the base of the ramp is 5 m/s, calculate his final speed at the end of the ramp?

Question

1. A skateboarder coasts at a constant velocity toward a ramp with a 15 angle, preparing for the big trick jump. If the frictionless ramp is 3m long, and his initial velocity at the base of the ramp is 5 m/s, calculate his final speed at the end of the ramp?

Answer 1

part of his K.E. becomes gravitational P.E. at the end of the ramp

the height of the end of the ramp is ... 3 m / sin(15º)

final K.E. = initial K.E. - gravitational P.E. =
... (1/2 m 5^2) - [m * 9.8 * 3 m / sin(15º)]

final speed = √[ 2 * final K.E. / m]

Answer 2

To calculate the skateboarder's final speed at the end of the ramp, we need to consider the conservation of energy.

First, let's break down the problem using the principle of conservation of energy:

1. The initial energy of the skateboarder is given by the kinetic energy at the base of the ramp.
2. The final energy of the skateboarder is given by the potential energy at the top of the ramp.
3. Since the skateboarder doesn't lose any energy during the motion (as there is no friction), the initial energy and the final energy should be equal.

Let's calculate the potential energy at the top of the ramp using the formula:

Potential Energy = m * g * h

Where:
m is the mass of the skateboarder (which is not given)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height of the ramp

Given that the ramp is 3m long and has an angle of 15 degrees, we can calculate the height (h) using trigonometry.

Height (h) = ramp length * sin(angle)

Now, let's calculate the potential energy at the top of the ramp.

Potential Energy = m * g * h = m * g * (ramp length * sin(angle))

Next, let's calculate the initial kinetic energy at the base of the ramp using the formula:

Initial Kinetic Energy = 0.5 * m * v^2

Where:
v is the initial velocity at the base of the ramp (which is given as 5 m/s)

Let's calculate the initial kinetic energy.

Initial Kinetic Energy = 0.5 * m * v^2 = 0.5 * m * (5^2)

Now, since the initial kinetic energy is equal to the potential energy, we can set the two equations equal to each other and solve for the final speed.

0.5 * m * (5^2) = m * g * (ramp length * sin(angle))

Simplifying the equation, we get:

0.5 * (5^2) = 9.8 * (3 * sin(15))

Now, solve for the final speed by rearranging the equation:

Final Speed = √(2 * (0.5 * (5^2) / m)

Please note that to get the final speed completely, we would need to know the mass of the skateboarder.