# Projectile Motion of Car Problem

• triamanda
In summary: Note that the car's velocity is constant in its x direction. Once you have found the time of flight t, use it in the equation for the horizontal distance traveled by the car in time t, X(t).
triamanda

## Homework Statement

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24 degrees below the horizontal. The parking break is defective, so the car rolls from rest down the incline with a constant acceleration on 4m/s2 and travels 50m to the edge of the ocean. The cliff is 30 m above the ocean.

a. What is the car's horizontal position relative to the base of the cliff when it lands in the ocean?

b. How long is the car in the air?

Vy2 = -2gΔy
Δy = -1/2g(Δt)2
Vy= -gΔt
Vx = Δx/Δt

## The Attempt at a Solution

Δt = square root (30sin(24)/(1/2)g) = 2.5s

However, I don't really think that's right. If someone could explain the process of solving the overall of equation, that would be extremely helpful.

...finals tomorrow.

triamanda said:

## Homework Statement

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24 degrees below the horizontal. The parking break is defective, so the car rolls from rest down the incline with a constant acceleration on 4m/s2 and travels 50m to the edge of the ocean. The cliff is 30 m above the ocean.

a. What is the car's horizontal position relative to the base of the cliff when it lands in the ocean?

b. How long is the car in the air?

Vy2 = -2gΔy
Δy = -1/2g(Δt)2
Vy= -gΔt
Vx = Δx/Δt

## The Attempt at a Solution

Δt = square root (30sin(24)/(1/2)g) = 2.5s

However, I don't really think that's right. If someone could explain the process of solving the overall of equation, that would be extremely helpful.

...finals tomorrow.

This problem is a bit complicated. First you must calculate the velocity of the car when it reaches the bottom of the incline just before it leaves the cliff. From that velocity vector which makes an angle of 24 degrees below the horizontal, you need to calculate the horizontal and vertical components of its velocity. Call these $V_0x$ and $V_0y$ respectively. Now take your coordinate axes to have their origin at the edge of the cliff where the car leaves. Choose the Y axis vertical, X axis horizontal. Then you need to simultaneously solve the kinematic equations of projectile motion:

$$X = X_0 + V_0x t + \frac{1}{2} a_x t^2$$

$$Y = Y_0 + V_0y t + \frac{1}{2} a_y t^2$$

Recall that $a_y = g$. What is $a_x$ ?

I understand your concern and the importance of finding the correct solution for this problem. Here is how I would approach it:

a. To find the car's horizontal position relative to the base of the cliff when it lands in the ocean, we can use the equation Vx = Δx/Δt. We know that the car travels 50m horizontally and we can calculate the time it takes to reach the edge of the ocean using the equation Δy = -1/2g(Δt)2. Using the given values, we can plug them into the equations and solve for Δt, which comes out to be approximately 3.2 seconds. Now, using this value of Δt, we can plug it into the equation Vx = Δx/Δt to find the horizontal position. This gives us a horizontal position of 160m relative to the base of the cliff.

b. To find the time the car is in the air, we can use the equation Δy = -1/2g(Δt)2 and plug in the values of Δy (30m) and g (4m/s2). Solving for Δt, we get a time of approximately 2 seconds.

I hope this helps you understand the process of solving this problem. Good luck on your finals!

## 1. What is projectile motion?

Projectile motion is the motion of an object that is projected into the air and then moves along a curved path due to the influence of gravity.

## 2. How is projectile motion of a car different from that of other objects?

Projectile motion of a car is different from that of other objects because the car is not simply thrown into the air, but moves along a curved path due to the force of the engine and the influence of gravity.

## 3. How is the initial velocity of the car determined?

The initial velocity of the car is determined by the speed and direction in which the car is launched or propelled.

## 4. What factors affect the trajectory of a car in projectile motion?

The trajectory of a car in projectile motion is affected by factors such as the initial velocity, the angle at which the car is launched, air resistance, and the force of gravity.

## 5. How can the maximum height and range of a car in projectile motion be calculated?

The maximum height and range of a car in projectile motion can be calculated using equations that take into account the initial velocity, launch angle, and gravitational force acting on the car.

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