A roller coaster reaches the top of the steepest hill with a speed of 7.0 km/h. It then descends the hill, which is at an average angle of 38^\circ and is 50.0 m long.

and the question is?

To determine the speed of the roller coaster at the bottom of the hill, we need to consider the conservation of mechanical energy. The mechanical energy of a moving object is the sum of its kinetic energy (KE) and potential energy (PE). At the top of the hill, all of the roller coaster's energy is in the form of potential energy, which is given by the equation:

PE = mgh

where m is the mass of the roller coaster, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the hill.

Since we only have the speed of the roller coaster at the top of the hill, we need to convert it to meters per second (m/s). To do this, we divide the speed in kilometers per hour by 3.6 (1 km/h = 1000 m/3600 s = 1/3.6 m/s).

Speed at the top of hill = 7.0 km/h = 7.0/3.6 m/s = 1.94 m/s

Now, to determine the height of the hill, we can use trigonometry. The average angle of the hill is given as 38 degrees, and the length of the hill is 50.0 m. We can find the height (h) using the equation:

h = l*sin(θ)

where l is the length of the hill, and θ is the angle of inclination.

Height of the hill, h = 50.0 m * sin(38°) ≈ 30.5 m

Now that we know the height of the hill, we can calculate the potential energy of the roller coaster at the top of the hill using the equation mentioned earlier. However, we also need the mass of the roller coaster to compute the potential energy. Without the mass provided in the problem, it is not possible to determine the exact value.

Therefore, we cannot calculate the speed of the roller coaster at the bottom of the hill without the mass information.