At the beginning of a roller coaster ride the car is staionary at the top of a 30m high hill and then begins to fall. Neglect any resistive forces. Calculate the speed of the car when it reaches the top of the second hill on the roller coaster. The second hill has abheight of 12m
Initial Energy=final PE + final KE
mg*30=mg*12+1/2 mv^2
calculate v.
To calculate the speed of the car when it reaches the top of the second hill, we can use the principle of conservation of energy.
At the top of the first hill, the car has gravitational potential energy (due to its height) and no kinetic energy (since it is stationary).
The gravitational potential energy (PE) is given by the formula: PE = m * g * h, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
So, at the top of the first hill, the car's potential energy is: PE1 = m * g * 30.
When the car reaches the top of the second hill, it has lost some of its potential energy but gained kinetic energy. The potential energy at this point is: PE2 = m * g * 12.
According to the conservation of energy principle, the change in potential energy is equal to the change in kinetic energy.
So, the change in kinetic energy (KE) is given by: ΔKE = PE1 - PE2.
ΔKE = (m * g * 30) - (m * g * 12)
= m * g * (30 - 12)
= m * g * 18.
Now, we know that kinetic energy is given by the formula: KE = (1/2) * m * v^2, where v is the velocity or speed of the car.
Since the velocity is the same for both hills, we can equate the two kinetic energies.
(1/2) * m * v1^2 = m * g * 18
Simplifying the equation, we get:
v1^2 = 2 * g * 18
v1^2 = 2 * 9.8 * 18
v1^2 = 352.8
v1 ≈ 18.77 m/s
So, the speed of the car when it reaches the top of the second hill is approximately 18.77 m/s.