Finding max. distance and time (projectile motion)

In summary: It will be measured in meters, and the time will be in seconds.In summary, John plans to drive a car off of one ramp and land on a similar opposing ramp. The ramps are slanted at 30 degrees and the car leaves one ramp at a speed of 30m/s. To successfully complete the stunt, the maximum distance between the ramps must be determined. In order to calculate this distance, the time that the car spends between the ramps must be determined first. Using the given speed and angle of the ramps, the time can be calculated using the equation t = d/v, where t is time, d is distance, and v is velocity. Once the time is calculated, the maximum distance between the ramps can be found by
  • #1
cvc121
61
1

Homework Statement


John plans to drive a car off of one ramp and land on a similar opposing ramp. The ramps are slanted at 30 degrees. His car leaves one ramp at a speed of 30m/s.

a) What is the maximum distance between the ramps for the stunt to succeed?
b) How much time does the car spend in the between ramps?

Homework Equations

The Attempt at a Solution


My attempt at the solution is shown below. Can anyone verify my work and see if I am on the right track? Note: I did question b) first because I needed that time value for a). Thanks. All help is very much appreciated!
 

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  • #2
cvc121 said:

Homework Statement


John plans to drive a car off of one ramp and land on a similar opposing ramp. The ramps are slanted at 30 degrees. His car leaves one ramp at a speed of 30m/s.

a) What is the maximum distance between the ramps for the stunt to succeed?
b) How much time does the car spend in the between ramps?

Homework Equations

The Attempt at a Solution


My attempt at the solution is shown below. Can anyone verify my work and see if I am on the right track? Note: I did question b) first because I needed that time value for a). Thanks. All help is very much appreciated!
The distance between ramps will not be measured in m/s.
 

1. How do you find the maximum distance of a projectile?

The maximum distance of a projectile can be found by using the formula d = v02sin(2θ)/g, where d is the maximum distance, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. This formula assumes ideal projectile motion and no air resistance.

2. What is the equation for finding the time of flight of a projectile?

The equation for finding the time of flight of a projectile is t = 2v0sin(θ)/g, where t is the time of flight, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. This formula also assumes ideal projectile motion and no air resistance.

3. Can you find the maximum distance and time of a projectile without knowing the launch angle?

No, the launch angle is a necessary component in calculating the maximum distance and time of a projectile. Without it, the equations for distance and time cannot be solved.

4. How does air resistance affect the maximum distance and time of a projectile?

Air resistance can decrease the maximum distance and time of a projectile. This is because air resistance creates a force that acts opposite to the direction of motion, slowing down the projectile. However, the effect of air resistance is dependent on the shape and size of the projectile, as well as other factors such as air density and temperature.

5. What are some real-world applications of projectile motion?

Projectile motion has many real-world applications, including sports (such as baseball, football, and golf), fireworks, and launching satellites into orbit. It is also used in physics experiments and in engineering design for things like catapults and cannons.

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