Calculating Final Velocity of a Car Over a Ramp

In summary, the conversation discusses a problem involving a car driving over a ramp and the speed at which it will hit the ground. One person provides their work and asks for verification. Another person points out that the vertical velocity and horizontal velocity must be added together to find the resultant velocity, and provides the formula for calculating it. The original person asks if a different formula would work, and the conversation ends with a final calculation being correct.
  • #1
Drakon25th
OK, many people in my class got a different answer from each other, so could someone verify my work for me please? Here's the problem:

A car (m=1000kg) driving at 20 m/s goes over a ramp angled at 37 degrees with a height of 5 m. How fast is the car traveling when it hits the ground 15 m below the end of the ramp?

my work:

Vyo = 20m/s ( sin37º)
Vyo = 12.0 m/s

Vy = sqrt(vyo^2 + 2gy)
Vy = sqrt ((12m/2)^2 + 2 * 9.8m/s^2 * 15 m)
Vy = 21 m/s

So my answer was 21 m/s

edit: my webspace is down right now so can't post pic

is this correct or am i doing something wrong?
 
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  • #2
You forgot something

When the car hits the ground, it is not traveling perfectly vertical. Remember, for projectile motion, the horizonal velocity remains constant. Therefore you must add the final vertical velocity and the final horizontal velocity together (note they are vectors) to get a resultant velocity, which is on an angle that you must also calculate based on these velocities.
 
  • #3
21 m/s is the velocity in the y direction. The resultant velocity vector (the velocity at which the car hits the ground) would be the sum of the vectors in the x and y directions.

The resultant vector would be: 12i -21j
The car would hit the ground at sqrt ( 21^2 + 12^2) m/s

The direction is given by arctan (21/12) S of E
 
  • #4
oohh, i see, thanks
 
  • #5
one question, could i use the formula:
sqrt ((.5Vo^2+gho-ghf)/.5) ?

what i mean:

sqrt ((.5 (20m/s)^2 + 9.8m/s^2 * 10m)/.5) = 24.4 m/s

Or would that not be right?
 

1. What is the final velocity of a car?

The final velocity of a car is the speed at which it is moving at the end of its motion.

2. How is the final velocity of a car calculated?

The final velocity of a car can be calculated by dividing the change in distance by the change in time. This can also be represented by the formula: V = (Xf - Xi) / (Tf - Ti), where V is the final velocity, X is the distance, and T is the time.

3. Does the mass of the car affect its final velocity?

Yes, the mass of the car does affect its final velocity. The heavier the car, the more force is needed to accelerate it to a certain speed, resulting in a slower final velocity. However, for a given force, a lighter car will have a higher final velocity than a heavier car.

4. Can the final velocity of a car be greater than its initial velocity?

Yes, the final velocity of a car can be greater than its initial velocity. This occurs when the car is accelerating or when there is a net force acting on the car in the direction of its motion.

5. How does friction affect the final velocity of a car?

Friction can decrease the final velocity of a car. When a car is moving on a surface with friction, some of its kinetic energy is converted into heat and sound energy, resulting in a decrease in speed and a lower final velocity.

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