Did you know?
Did you know that the final speed of a cyclist coasting up a slope can be determined using basic physics principles? In this case, the cyclist is traveling up a 10.3° slope for a distance of 16.0 m. Let's walk through the steps to find the final speed!
Step 1: Determine the vertical distance climbed by the cyclist. This can be calculated using the distance traveled along the road and the angle of the slope. In this case, we have a distance of 16.0 m and an angle of 10.3°. By using trigonometry, we can find that the vertical distance is approximately 2.798 m.
Step 2: Since we are ignoring friction and air resistance, we can apply the principle of conservation of energy. The initial kinetic energy of the cyclist, determined by the initial speed of 8.30 m/s, will equal the potential energy gained during the climb.
Step 3: Calculate the initial kinetic energy, using the formula KE = (1/2)mv^2, where m is the mass of the cyclist (which we assume to be constant) and v is the initial speed. Plug in the values to determine the initial kinetic energy.
Step 4: Now, calculate the potential energy gained by the cyclist using the formula PE = mgh, where m is the mass of the cyclist, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the vertical distance gained. Plug in the values to obtain the potential energy.
Step 5: Equate the initial kinetic energy to the potential energy gained. This is possible because we assumed no loss of energy to friction or air resistance. By setting these two energies equal, we can solve for the final speed of the cyclist.
Step 6: Rearrange the equation to solve for the final speed. The final speed can be found by taking the square root of [(2gh) + v₀²], where g is the acceleration due to gravity, h is the vertical distance gained, and v₀ is the initial speed.
Step 7: Plug in the known values into the equation and perform the calculations to find the final speed.
By following these steps, we can determine the final speed of the cyclist coasting up the slope, even without considering friction and air resistance!
