# Calculating Minimum Speed for a Successful River Jump

• DannyDon
In summary, the motorcyclist must have a minimum speed to successfully jump across the river and will be in the air for a certain amount of time.
DannyDon

## Homework Statement

A stunt motorcyclist has to jump across a river 7.0 m wide from a ramp on one side with incline of 10 degrees. (a) What minimum speed the motorcycle must have to successfully land on the opposite side of the river? (b) How long will the motorcyclist be in the air? (Assume equal elevation on the both sides of the river, ignore air resistance)

## The Attempt at a Solution

I have no idea how to go about this, I've tried going through all of the kinematic equations with the 2 variables given. I'm assuming the extra information given after part (b) also relates to part (a) otherwise it would be impossible to solve? So my understanding is that there are 2 ramps on either side of the river, both of which have an incline of 10 degrees or am I misinterpreting the question?

DannyDon said:

## Homework Statement

A stunt motorcyclist has to jump across a river 7.0 m wide from a ramp on one side with incline of 10 degrees. (a) What minimum speed the motorcycle must have to successfully land on the opposite side of the river? (b) How long will the motorcyclist be in the air? (Assume equal elevation on the both sides of the river, ignore air resistance)

## The Attempt at a Solution

I have no idea how to go about this, I've tried going through all of the kinematic equations with the 2 variables given. I'm assuming the extra information given after part (b) also relates to part (a) otherwise it would be impossible to solve? So my understanding is that there are 2 ramps on either side of the river, both of which have an incline of 10 degrees or am I misinterpreting the question?

PF rules require that you show your work; saying you have no idea how to go about this is not considered to be a solution attempt.

What equations are there in your book/notes about projectile motion with initial angle θ relative to the horizontal? Specifically look for the equations of the horizontal and vertical displacement (distance).

From the description of the problem we can't be sure about the existence of the 2nd ramp. Is there a figure/scheme that accompanies this problem? In my opinion I don't think that the existence of the 2nd ramp is implied by the other data of the problem.

I think some assumptions are required. For example if the ramp was several hundred feet long the take off point would be quite high in relation to a landing point with no ramp. That would effect the minimum speed needed.

I think the angle of the ramp is only intended to give you the take off angle. So I would treat it as a simple projectile motion problem from ground level to ground level.

DannyDon said:
So my understanding is that there are 2 ramps on either side of the river, both of which have an incline of 10 degrees
As others have written, you are probably supposed to assume take off and landing are at the same height, so, yes, you can treat it as two identical ramps.

Delta2
haruspex said:
As others have written, you are probably supposed to assume take off and landing are at the same height, so, yes, you can treat it as two identical ramps.

I initially thought that this point was the "mini-trap" of this assignment, but then I saw that there is not enough data given to calculate the height from the launch ramp, so either the OP forgot to tell us some additional data (like for example what is the horizontal length of the ramp) or we ll have to assume as you say.

## 1. What is minimum speed and why is it important?

Minimum speed refers to the lowest velocity at which an object can move without stalling, falling, or failing to perform its function. It is important because it helps determine the optimal speed for an object to function efficiently and safely.

## 2. How is minimum speed calculated?

Minimum speed can be calculated by considering factors such as the weight of the object, the air resistance or drag force acting on the object, and the force or power of the engine or propulsion system. These factors are used to determine the minimum amount of energy needed to overcome the forces acting against the object and maintain its motion.

## 3. Can minimum speed vary for different objects?

Yes, minimum speed can vary for different objects depending on their size, shape, weight, and other factors. For example, a small airplane may have a lower minimum speed compared to a larger airplane due to differences in their aerodynamic designs and engine power.

## 4. How does altitude affect minimum speed?

As altitude increases, the air density decreases, which can affect the minimum speed of an object. This is because air density affects the amount of lift and drag forces acting on the object, which in turn can impact the minimum amount of energy needed to maintain motion.

## 5. How can minimum speed be tested or measured?

Minimum speed can be tested or measured through experiments or simulations that take into account the various factors affecting an object's motion, such as weight, air resistance, and engine power. This can help determine the minimum speed at which the object can function properly and safely. Real-life tests can also be conducted using specialized equipment to measure an object's speed and performance under different conditions.

• Introductory Physics Homework Help
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
23
Views
469
• Introductory Physics Homework Help
Replies
2
Views
16K
• Introductory Physics Homework Help
Replies
4
Views
7K
• Introductory Physics Homework Help
Replies
2
Views
5K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
8K