# Projectile Motion in 2D: Solving for Maximum Range in Inclined Planes

• kshitij
In summary, The conventional method for solving a question using the formula for maximum range of a projectile in an inclined plane may not always work for objective problems. In cases where α=0, only one option may match, but it may not necessarily be the correct answer. This is because the given question does not have any restrictions on α and it could take any value, so the answer should be consistent for all values of α. In the flat case, both answers B and D fit because u1 and u2 are the same. This is because in the α=0 case, R1 and R2 are equal, so their speeds must also be the same.

#### kshitij

Homework Statement
Three particles are projected in the air with the minimum possible speeds (particle at point A with u1,at B with u2 and at point C with u3), such that the first goes from A to B, the second goes from B to C and the third goes from C to A. Points A and C are at the same horizontal level. The two inclines make the same angle α with the horizontal, as shown. The relation among the projection speeds of the three particles is
(see attachment)
Relevant Equations
Range of a projectile=(u^2*sin2α)/g
I know the conventional method for solving this question using the formula for maximum range of a projectile in an inclined plane, but since it is an objective problem, if we consider a non general case where α=0, then clearly we can see that (see attachment) only one option matches which unfortunately isn't the right answer. I would like to know that why doesn't this method work since in the given question there is no restriction on α, it could take any value, so the given answer must be consistent for all values of α. What am I missing, is there a catch in the part that they are projected with minimum possible speed, if so then what should be the condition so that we get the correct answer for the α=0 case?

In the flat case, u1 and u2 are the same, so answers B and D both fit.

kshitij
haruspex said:
In the flat case, u1 and u2 are the same, so answers B and D both fit.
That's interesting, but I still don't get why they should be the same?

kshitij said:
That's interesting, but I still don't get why they should be the same?
Why what are the same? u1 and u2 in the α=0 case?

kshitij
haruspex said:
Why what are the same? u1 and u2 in the α=0 case?
Yes, I was asking why is u1 and u2 same in the α=0 case? But know I get it as from geometry R1 and R2 are equal so their speeds must be same. Thank you so much, I was stuck with this problem for quite some time

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## 1. What is projectile motion in 2D?

Projectile motion in 2D is a type of motion where an object is launched into the air and moves along a curved path under the influence of gravity. It is a combination of horizontal and vertical motion.

## 2. How do you solve for maximum range in inclined planes?

To solve for maximum range in inclined planes, you can use the equations of motion and trigonometry to find the initial velocity and launch angle that will result in the maximum horizontal distance traveled by the object.

## 3. What factors affect the maximum range in inclined planes?

The maximum range in inclined planes is affected by the initial velocity, launch angle, and the angle of the incline. Other factors such as air resistance and friction may also have an impact.

## 4. Can the maximum range be greater in inclined planes compared to flat surfaces?

Yes, the maximum range can be greater in inclined planes compared to flat surfaces. This is because the angle of the incline can increase the horizontal component of the velocity, resulting in a longer distance traveled.

## 5. How is projectile motion in 2D used in real life?

Projectile motion in 2D is used in various real-life applications, such as sports (e.g. throwing a ball or shooting a basketball), fireworks displays, and military artillery. It is also used in physics experiments and simulations to understand and analyze the motion of objects under the influence of gravity.