Projectile Motion of Car and Cliff

In summary, the conversation discusses a car parked on a cliff with a defective brake, rolling down an incline and falling into the ocean. The problem involves finding the car's position relative to the base of the cliff and the time it takes for the car to reach the ocean. The equations used include displacement, velocity, and acceleration. The final answers are given as a horizontal displacement of 32.5 m and a time of 1.78 seconds.
  • #1
Graceful169
1
0

Homework Statement


A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0º below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4.00 m/s² for a distance of 50.0 m to the cliffs edge. The cliff is 30.0 m above the ocean. Find (a) the cars position relative to the base of the cliff when the car lands in the ocean, and (b) the length of time the car is in the air.


Homework Equations


dy = ½• g•t2 + vo• t + h
vy = a•t + vo
dx = vx•t + ho
vx = constant


The Attempt at a Solution


The answers are giving to me as a)dx = 32.5 m and b) t = 1.78 s, but I have tried greatly to get there and no matter how I plug in the data I never seem to get it right
 
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  • #2
1) Car starts from rest. Acceleration is given. Displacement is given. Find the final velocity vf at the edge of the cliff.
2) Resolve vf into vertical and horizontal components.
3) Find the time to reach the ocean
4) Find the horizontal displacemnt.
 
  • #3
.

I would first verify the given information and equations to ensure their accuracy. I would also clarify any uncertainties or assumptions made in the problem.

Next, I would approach the problem by breaking it down into smaller components and using the equations of motion to analyze each component separately. For example, I would first calculate the time it takes for the car to reach the cliff's edge using the equation vy = a•t + vo, where vy is the final vertical velocity (0 m/s), a is the acceleration (-4.00 m/s²), and vo is the initial vertical velocity (0 m/s). Solving for t, I get t = 5 seconds.

Then, I would calculate the horizontal distance the car travels using the equation dx = vx•t + ho, where dx is the horizontal distance (50 m), vx is the constant horizontal velocity (unknown), t is the time calculated in the previous step (5 s), and ho is the initial horizontal position (0 m). Solving for vx, I get vx = 10 m/s.

Using the calculated values for t and vx, I can then use the equation dy = ½•g•t2 + vo•t + h to find the vertical distance the car falls before hitting the ocean. Plugging in g = -9.8 m/s², t = 5 s, vo = 0 m/s, and h = 30 m, I get dy = -32.5 m.

Therefore, the car's position relative to the base of the cliff when it lands in the ocean is 32.5 m. This aligns with the given answer of 32.5 m.

To calculate the time the car is in the air, I can use the same equation dy = ½•g•t2 + vo•t + h and solve for t. Plugging in dy = -30 m, g = -9.8 m/s², vo = 0 m/s, and h = 30 m, I get t = 1.78 s. This also aligns with the given answer of 1.78 s.

In conclusion, by breaking down the problem into smaller components and using the equations of motion, I was able to verify the given answers for the car's position relative to the base of the cliff and the time it spends in the air.
 

1. What is projectile motion?

Projectile motion is the motion of an object that is projected into the air and then moves freely under the influence of gravity. It is a combination of horizontal and vertical motion, where the object follows a curved path called a parabola.

2. How does projectile motion apply to a car and a cliff?

In the case of a car and a cliff, the car is the projectile and the cliff is the vertical surface it is projected towards. The car follows a curved path as it moves horizontally off the cliff and then falls vertically towards the ground due to the force of gravity.

3. What factors affect the projectile motion of a car and cliff?

The factors that affect the projectile motion of a car and cliff include the initial velocity of the car, the angle at which it is projected, the mass of the car, and the effects of air resistance. The height of the cliff and the force of gravity also play a role in the motion.

4. How can we calculate the time of flight for a car projected off a cliff?

The time of flight for a car projected off a cliff can be calculated using the formula t = 2v₀sinθ/g, where t is the time of flight, v₀ is the initial velocity of the car, θ is the angle of projection, and g is the acceleration due to gravity (9.8 m/s²).

5. What is the maximum height reached by a car projected off a cliff?

The maximum height reached by a car projected off a cliff can be calculated using the formula h = (v₀sinθ)²/2g, where h is the maximum height reached, v₀ is the initial velocity of the car, θ is the angle of projection, and g is the acceleration due to gravity. This value will depend on the initial conditions of the car's projection.

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