# Will Your Friend Make the Jump? Analyzing Parabolic Motion in a Motorcycle Stunt

• thegreengineer
In summary, the rider could potentially reach the other bank if he launches at a speed greater than 12 m/s and is above the required height.
thegreengineer
Well people, this is the given problem:

Your friend is trying to impress his girlfriend jumping a river that is 10.5 m long (this is the horizontal range). Your friend wants you to recommend him how to improve the jump as he tells you that the jumping point (the cliff from which your friend wants to jump) is 3 m above the river as it has an inclination angle of 30° (with respect to x axis). The other point to reach (i.e. the other cliff) is 4 m above the river. If the motorcycle's max velocity that can run is 12 m/s, would you recommend him to jump or not? Justify your answer.Ok people so this is parabolic motion, even though we already know the equations of motion for constant acceleration, I'm only going to write the ones concerning with parabolic motion which as I saw in school are:

$R=\frac{(v_{0})^{2}(\textbf{sin}(2θ))}{g}$
$y_{max}=\frac{(v_{0})^{2}(\textbf{sin}^{2}(θ))}{2g}$
$t=\frac{2(v_{0})(\textbf{sin}(θ))}{g}$

In which R is the range, ymax is the maximum height, and t is the time that it took in the air.

Ok, so my main problem is to determine whether this guy reaches the cliff or not. According to what I've got in the data I was able to determine the range which resulted in:

$R=\frac{(12\frac{m}{s})^{2}(\textbf{sin}(2(30°)))}{9.81\frac{m}{s^{2}}}=12.73 m$

Now my main problem is that even though I found that the range is larger than what the river is 10.5 m long; we can assume that this guy will make it to the other side. Now to prove that is to find that he can reach it in vertical terms (I mean, that he won't be falling short and he will reach the other side without crashing)I need to find if he makes it or not because I don't feel secure saying it just finding that the range was larger than the river's length.

Last edited by a moderator:
MarcusAu314 said:
Well people, this is the given problem:

Your friend is trying to impress his girlfriend jumping a river that is 10.5 m long (this is the horizontal range). Your friend wants you to recommend him how to improve the jump as he tells you that the jumping point (the cliff from which your friend wants to jump) is 3 m above the river as it has an inclination angle of 30° (with respect to x axis). The other point to reach (i.e. the other cliff) is 4 m above the river. If the motorcycle's max velocity that can run is 12 m/s, would you recommend him to jump or not? Justify your answer.

Ok people so this is parabolic motion, even though we already know the equations of motion for constant acceleration, I'm only going to write the ones concerning with parabolic motion which as I saw in school are:

$R=\frac{(v_{0})^{2}(\textbf{sin}(2θ))}{g}$
$y_{max}=\frac{(v_{0})^{2}(\textbf{sin}^{2}(θ))}{2g}$
$t=\frac{2(v_{0})(\textbf{sin}(θ))}{g}$

In which R is the range, ymax is the maximum height, and t is the time that it took in the air.

Ok, so my main problem is to determine whether this guy reaches the cliff or not. According to what I've got in the data I was able to determine the range which resulted in:

$R=\frac{(12\frac{m}{s})^{2}(\textbf{sin}(2(30°)))}{9.81\frac{m}{s^{2}}}=12.73 m$

Now my main problem is that even though I found that the range is larger than what the river is 10.5 m long; we can assume that this guy will make it to the other side. Now to prove that is to find that he can reach it in vertical terms (I mean, that he won't be falling short and he will reach the other side without crashing)

I need to find if he makes it or not because I don't feel secure saying it just finding that the range was larger than the river's length.

Hi MarcusAu314, Welcome to Physics Forums.

Your range equation applies to a projectile launched and landing on a flat horizontal plane. here you've got a difference in elevation to deal with. The max height equation doesn't seem applicable since the rider will attain that somewhere over the river. So really you need something else to work with.

Why don't you try to determine the height of the rider at the instant he reaches the other bank, given that he launches at 30° at his maximum speed? Is he above or below the required height? Start by listing the standard projectile motion equations.

Oh, and next time please be sure to keep and use the formatting template when you start a new thread.

Ok thanks for the advice and sorry, I'm new to this site.

## 1. What is parabolic motion?

Parabolic motion is the motion of an object in a curved path, where the acceleration due to gravity is constant and acts perpendicular to the direction of motion. This type of motion is often seen in projectile motion, where an object is launched at an angle and follows a parabolic trajectory.

## 2. What are the key equations for solving parabolic motion problems?

The key equations for solving parabolic motion problems are the equations of motion, also known as the kinematic equations. These include the equations for displacement, velocity, acceleration, and time, which are derived from the basic principles of motion and can be used to solve for unknown quantities in parabolic motion problems.

## 3. How do you find the maximum height and range of a projectile in parabolic motion?

To find the maximum height of a projectile, you can use the equation for vertical displacement, setting the initial vertical velocity to zero. The range of a projectile can be found using the equation for horizontal displacement, where the time of flight is doubled and multiplied by the initial horizontal velocity.

## 4. What factors affect the trajectory of a projectile in parabolic motion?

The factors that affect the trajectory of a projectile in parabolic motion are the initial velocity, angle of launch, and the acceleration due to gravity. Changing any of these factors will result in a different trajectory, with a higher initial velocity and smaller launch angle resulting in a longer range, and a higher launch angle resulting in a higher maximum height.

## 5. How does air resistance affect parabolic motion?

Air resistance, also known as drag, can have a significant effect on parabolic motion. It acts in the opposite direction of motion and reduces the speed and distance traveled by a projectile. In some cases, air resistance can also cause the trajectory of a projectile to deviate from a perfect parabolic shape.

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