Projectile Motion on a Ramp: Solving for Distance, Time, and Velocity

In summary, a toy car is driven off a level platform at the top of a ramp with an initial velocity of 3.26 m/s and an angle of 34.7° with respect to the horizontal direction. To determine how far the car travels horizontally before landing on the ramp, as well as the time it is in the air and the magnitude of its velocity just before landing, standard kinematics equations can be used. By setting up separate equations for horizontal and vertical motion and using the known angle of the ramp to eliminate a variable, the time of touching down can be solved for and used to calculate the other unknown quantities.
  • #1
Becca93
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Homework Statement


A toy car is driven horizontally off of a level platform at the top of a ramp as shown. The velocity of the car just as it leaves the ramp is 3.26 m/s. The angle of the ramp with respect to the horizontal direction, theta, is 34.7 °.

How far does the car travel horizontally before landing on the ramp?
How long is the car in the air?
What is the magnitude of the car's velocity just before it lands on the ramp?


Homework Equations


Standard kinematics equations.
 

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  • #2
Nearly all 2D motion problems can be solved by this method:
Make two headings for "horizontal" and "vertical".
In each case, ask yourself what kind of motion is involved and write down the basic formulas for the motion. You should have one formula for horizontal and two (one v= and one d= ) for the vertical.
Fill in the numbers you know in all three formulas.
In this case, you also have a relationship between y and x when the car touches the ramp because of the straight ramp at a known angle. Use that to eliminate y or x in the three formulas.
Now you should be able to solve one of the formulas and find something, hopefully time of touching down.
 

Related to Projectile Motion on a Ramp: Solving for Distance, Time, and Velocity

1. How does the angle of the ramp affect the distance a projectile lands?

The angle of the ramp determines the horizontal distance a projectile will travel before landing. The steeper the angle, the shorter the distance, while a lower angle will result in a longer distance. This is because a steeper angle increases the vertical component of the projectile's velocity, causing it to spend more time in the air before hitting the ground.

2. What is the relationship between the initial velocity and the angle of the ramp?

The initial velocity of a projectile does not directly affect the angle of the ramp. However, the angle of the ramp can impact the initial velocity needed for the projectile to reach a certain distance. For example, a steeper ramp will require a higher initial velocity for the projectile to reach the same distance as a shallower ramp.

3. How does the mass of the projectile affect its landing on a ramp?

The mass of the projectile does not have a significant impact on its landing on a ramp. As long as the initial velocity and angle of the ramp remain constant, the mass of the projectile will only affect its trajectory in terms of height and distance traveled.

4. What factors affect the time it takes for a projectile to land on a ramp?

The time it takes for a projectile to land on a ramp is affected by the initial velocity, the angle of the ramp, and the acceleration due to gravity. The steeper the angle and the higher the initial velocity, the longer the projectile will spend in the air. Additionally, the acceleration due to gravity will affect the speed at which the projectile falls towards the ramp.

5. Can a projectile land on a ramp at a perfectly perpendicular angle?

No, it is not possible for a projectile to land on a ramp at a perfectly perpendicular angle. This is because the ramp would then have to be completely vertical, and the projectile would simply slide down without making contact with the ramp. In order for a projectile to land on a ramp, there must be some angle between the ramp and the horizontal surface.

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