Question

A cyclist coasts up a 7.00 ° slope, traveling 17.0 m along the road to the top of the hill. if the cyclist’s initial speed is 9.75 m/s, what is the final speed? ignore friction and air resistance.

Answer 1

To find the final speed of the cyclist coasting up a slope, we can use the principle of conservation of energy. The final speed can be calculated using the equation: v_final = sqrt(v_initial^2 + 2gh), where v_initial is the initial speed, g is the acceleration due to gravity, and h is the vertical height traveled.

Step-by-step explanation:

To find the final speed of the cyclist, we can use the principle of conservation of energy which states that the total mechanical energy of a system remains constant if there are no external forces acting on it. In this case, the cyclist is only subject to the gravitational force, so we can equate the initial kinetic energy to the final potential energy:

KEinitial + PEinitial = KEfinal + PEfinal

Since the cyclist starts with an initial speed and reaches the top of the hill, the final potential energy is zero. Plugging in the given values:

0.5 * m * vinitial2 + m * g * h = 0.5 * m * vfinal2

where m is the mass of the cyclist, vinitial is the initial speed, g is the acceleration due to gravity (9.8 m/s²), h is the vertical height traveled. Solving for vfinal:

vfinal = sqrt(vinitial2 + 2 * g * h)

Now we can substitute the given values to calculate the final speed.