Max RANGE of a projectile thrown from the top of a ramp.

In summary, the maximum range of a projectile thrown from the top of a ramp is affected by several factors, including the initial velocity, angle of launch, air resistance, and height of the ramp. A higher initial velocity and a launch angle of around 45 degrees are optimal for achieving maximum range. Air resistance can decrease the maximum range, and the height of the ramp can either increase or decrease the range depending on its height.
  • #1
VyRianS
7
0

Homework Statement



A projectile is thrown from the top of the ramp. Find the angle [itex]\theta[/itex] of the throw that gives a max range R down the ramp. [itex]\phi[/itex] is the angle made from the base of the ramp to the x-axis.

2. The attempt at a solution

Tried a number of times but failed to get anything that seemed moderately appropriate, i.e. getting long equations that are obviously too complex to be the answer.

Appreciate the help.

Thanks.
 
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  • #2
Did you use a trig identity to simplify it?
 

Related to Max RANGE of a projectile thrown from the top of a ramp.

What factors affect the maximum range of a projectile thrown from the top of a ramp?

The maximum range of a projectile thrown from the top of a ramp is affected by several factors, including the initial velocity of the projectile, the angle at which it is thrown, the air resistance, and the height of the ramp.

How does the initial velocity of the projectile affect its maximum range?

The initial velocity of the projectile has a direct impact on its maximum range. The higher the initial velocity, the farther the projectile will travel. This is because a higher initial velocity means the projectile has more kinetic energy, allowing it to overcome air resistance and travel a greater distance.

What is the optimal angle for throwing a projectile from the top of a ramp to achieve maximum range?

The optimal angle for achieving maximum range varies depending on the initial velocity of the projectile. Generally, a launch angle of around 45 degrees will result in the maximum range. However, this may differ based on the specific conditions and factors affecting the projectile's flight.

What effect does air resistance have on the maximum range of a projectile thrown from the top of a ramp?

Air resistance can significantly impact the maximum range of a projectile thrown from the top of a ramp. As the projectile travels through the air, it experiences a force of drag due to air resistance, which slows it down. The higher the air resistance, the shorter the maximum range of the projectile will be.

How does the height of the ramp affect the maximum range of a projectile thrown from the top?

The height of the ramp also plays a role in the maximum range of a projectile. The higher the ramp, the longer the projectile has to accelerate and gain velocity before reaching the ground. This can result in a longer maximum range. However, if the ramp is too high, the projectile may reach its maximum height before it reaches the ground, resulting in a shorter range.

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