Assume the height of a hill is 50m, calculate:
a.the velocity of a car at the bottom ofg the hill
b.the height at which it will have half the speed. Assume the car starts from rest at the top of the hill.
A hill is of height 50 meters calculate (a)the velocity of the car at the bottom of the hill.(2)the height at which it will have half d speed.Assume the car starts from rest at the top of the hill
H=5om, v=?
P.E =K. E
Mgh =1/2mv^2
10× 50m =v^2 /2
2×10×50 =v^2
V = √1000
V=31. 62m/s
1/2 of speed (v)
1/2 × 31.62=15.81
P.E↓1 + K.E↓1=P.E↓2+K.E↓2
Mgh+ 1/2 mu^2 = mgh +1/2 mv^2
M×10×50= m×10h+ 1/2m × 15.81^2
Tired of typing☺️🙄🙄
To calculate the velocity of a car at the bottom of a hill, we need to use the principle of conservation of energy. We know that the car starts from rest at the top of the hill, so it has no initial kinetic energy.
a. To calculate the velocity, we can equate the potential energy at the top of the hill to the kinetic energy at the bottom. The potential energy is given by the formula:
Potential Energy (PE) = m * g * h
where m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the hill.
Since the car starts from rest at the top, its initial kinetic energy is zero:
Initial Kinetic Energy (KEi) = 0
At the bottom of the hill, the final kinetic energy is given by:
Final Kinetic Energy (KEf) = (1/2) * m * v^2
where v is the velocity of the car at the bottom.
By equating the potential energy at the top to the kinetic energy at the bottom, we have:
PE = KEf
m * g * h = (1/2) * m * v^2
Simplifying the equation, we get:
v = √(2 * g * h)
Substituting the given values of g = 9.8 m/s^2 and h = 50 m, we can calculate the velocity at the bottom of the hill:
v = √(2 * 9.8 * 50)
v ≈ 31.3 m/s
Therefore, the velocity of the car at the bottom of the hill is approximately 31.3 m/s.
b. To determine the height at which the car will have half the speed, we can use the formula derived in part a:
v = √(2 * g * h)
We need to find the height (h) at which the velocity (v) is half of the velocity at the bottom of the hill (31.3 m/s).
Let's denote the height at which the car will have half the speed as h1. We can set up the following equation:
31.3/2 = √(2 * g * h1)
Squaring both sides of the equation, we get:
(31.3/2)^2 = 2 * g * h1
Simplifying further:
h1 = (31.3/2)^2 / (2 * g)
Substituting the value of g = 9.8 m/s^2, we can calculate the height:
h1 = (31.3/2)^2 / (2 * 9.8)
h1 ≈ 40.3
Therefore, the height at which the car will have half the speed is approximately 40.3 meters.
You can only make this calculation if you assume that the car is "coasting" in neutral with zero friction. These are rather unrealistic assumptions for driving a car.
I suggest you make these assumptions anyway use conservation of energy to predict the speeds.