A skateboarder at a skate park rides along the path. If the speed of the skateboarder at point A is v=1.4 m/s what is her speed at point B?
Point A = 2.7 m & Point B=1.0 m
To find the speed of the skateboarder at point B, we can use the principle of conservation of energy. According to this principle, the sum of the kinetic energy and potential energy at any two points of the skateboarder's motion should be the same, assuming no external forces (such as friction or air resistance) act on the system.
First, let's calculate the initial potential energy at point A. The potential energy of an object at a certain height is given by the formula:
Potential Energy = m * g * h
Where:
m is the mass of the object (skateboarder)
g is the acceleration due to gravity (~9.8 m/s^2)
h is the vertical distance from the point of reference (in this case, the ground)
Since we don't have the mass of the skateboarder, we can assume it to be constant and cancel it out from the equation.
At point A, the height is given as 2.7 m. So the potential energy at point A is:
Potential Energy_A = g * h_A
= 9.8 * 2.7 J
Next, let's calculate the final potential energy at point B. The height at point B is given as 1.0 m. So the potential energy at point B is:
Potential Energy_B = g * h_B
= 9.8 * 1.0 J
According to the conservation of energy principle, the sum of the initial kinetic energy (at point A) and the initial potential energy (at point A) should be equal to the sum of the final kinetic energy (at point B) and the final potential energy (at point B).
Since the skateboarder's mass is constant, we can cancel it out from the equation:
Initial Kinetic Energy_A + Potential Energy_A = Final Kinetic Energy_B + Potential Energy_B
Since we know the initial speed (v_A = 1.4 m/s) and the final height, we can calculate the final kinetic energy and hence find the final speed.
The initial kinetic energy at point A is given by the formula:
Initial Kinetic Energy_A = 0.5 * m * v_A^2
Now we can substitute the given values to find the initial kinetic energy at point A.
Next, rearrange the equation to solve for the final kinetic energy at point B:
Final Kinetic Energy_B = Initial Kinetic Energy_A + Potential Energy_A - Potential Energy_B
Finally, we can calculate the final speed (v_B) using the formula for kinetic energy:
Final Kinetic Energy_B = 0.5 * m * v_B^2
Rearrange the above equation to solve for v_B:
v_B = sqrt(2 * Final Kinetic Energy_B / m)
Substitute the calculated value of the final kinetic energy and the mass to find the final speed at point B.
To determine the skateboarder's speed at point B, we can use the formula for speed:
Speed = Distance / Time
First, we need to calculate the time it takes for the skateboarder to travel from point A to point B. We can use the equation:
Time = Distance / Speed
Given that the distance between point A and point B is 2.7 m - 1.0 m = 1.7 m, and the initial speed at point A is v = 1.4 m/s, we can calculate the time as follows:
Time = 1.7 m / 1.4 m/s
Time = 1.214 s
Now, we can calculate the skateboarder's speed at point B using the formula:
Speed = Distance / Time
Since the distance at point B is 1.0 m, and the calculated time is 1.214 s, the speed at point B can be calculated as follows:
Speed = 1.0 m / 1.214 s
Speed ≈ 0.822 m/s
Therefore, the skateboarder's speed at point B is approximately 0.822 m/s.