How to find the horizontal range of the car rolling off an inclined cliff

In summary, the problem involves a car parked on an inclined cliff with a 14 degree angle and defective emergency brakes. The car rolls down the incline and reaches a velocity of 5 m/s at the edge of the cliff, which is 34.6 m above the ocean. The task is to determine the distance of the car from the base of the cliff when it hits the ocean, using the acceleration of gravity as 9.8 m/s^2. Two equations are mentioned as potential solutions, but the validity of their use is uncertain due to the angle of the cliff and undefined variables. The initial speed of the car is also questioned, as it is unclear if it refers to the horizontal or vertical components of velocity.
  • #1
IantheJay
1
0

Homework Statement



A car is parked near a cliff overlooking the
ocean on an incline that makes an angle of
14 with the horizontal. The negligent driver
leaves the car in neutral, and the emergency
brakes are defective. The car rolls from rest
down the incline and has a velocity 5 m/s
when it reaches the edge of the cliff. The cliff
is 34.6 m above the ocean. How far is the car from the base of the cliff
when the car hits the ocean? The acceleration
of gravity is 9.8 m/s2 .
Answer in units of m

Homework Equations



d = (Vi)t + .5at^2

or

[d][horizontal] = (Vi * √(2 height)) / [a][gravity]

The Attempt at a Solution



I would like to be able to plug into the second equation, but I'm not sure if the angle of the cliff would not allow me to do this. I am kind of unsure if these are even the right equations to be using.
 
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  • #2
Since you haven't defined any of your variables, it is impossibleto say if you are doing this right or not. I do notice that you Vi in both horizontal and vertical equations. If I were to guess that you are talking about "initial speed" surely you don't mean that the vertical and horizontal components of velocity? It the initial speed (strictly speaking, not velocity which is a vector quantity) was 5 m/s what are the horizontal and vertical components of velocity?
 

1. What is the formula for finding the horizontal range of a car rolling off an inclined cliff?

The formula for finding the horizontal range of a car rolling off an inclined cliff is R = (v2sin2θ)/g, where R is the horizontal range, v is the initial velocity of the car, θ is the angle of the incline, and g is the acceleration due to gravity.

2. How is the angle of the incline measured when calculating the horizontal range?

The angle of the incline is typically measured in degrees using a protractor. Alternatively, it can also be calculated using trigonometric functions, such as sine, cosine, or tangent.

3. Can the horizontal range of a car rolling off an inclined cliff be negative?

No, the horizontal range cannot be negative. It represents the distance traveled by the car in a horizontal direction, so it is always a positive value.

4. Is air resistance considered when calculating the horizontal range of a car rolling off an inclined cliff?

In most cases, air resistance is neglected when calculating the horizontal range. This is because the impact of air resistance on the motion of the car is minimal compared to the effects of gravity and the initial velocity.

5. Does the mass of the car affect the horizontal range when rolling off an inclined cliff?

Yes, the mass of the car does affect the horizontal range. A heavier car will have a larger force of gravity acting on it, which can result in a longer horizontal range compared to a lighter car. However, other factors such as the initial velocity and angle of incline also play a significant role in determining the horizontal range.

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