# Projectile launch point problem

• SA32
In summary, the conversation discusses a projectile question where a projectile is fired at an angle and hits the ground after a certain amount of time. The first part of the question involves finding the difference in height between the launch point and landing point, with a lower launch point expressed as a negative number. The second part asks for the maximum height above the launch point that the projectile reaches. Using the formula for maximum height, it is determined that the vertical component of velocity at the maximum height is zero, and the formula for final velocity is used to solve for the unknown.
SA32
I'm having some difficulty with a projectiles question.

"A projectile is fired with an initial speed of 26.0 m/s at an angle of 40.0 degrees above the horizontal. The object hits the ground 8.00 s later."

The first part of the question is: "How much higher or lower is the launch point relative to the point where the projectile hits the ground?
Express a launch point that is lower than the point where the projectile hits the ground as a negative number."

Which I already found out using y=(viy)(t)-(1/2)(g)(t^2)

Substituting the given numbers, I get -180 m, which would be the case if the landing point was below the launch point. Since the question wants a launch point lower than the landing point, the answer is 180 m.

The second part, where I'm having trouble: "To what maximum height above the launch point does the projectile rise?"

What I have,

x=(26)(cos(40))(t)
y=(26)(sin(40))(t)-(1/2)(g)(t^2)

I can't substitute 180 m or 8 s because those numbers apply to the landing point, and I'm looking for ymax so I end up with three unknowns in two equations, which I cannot solve. I don't know how to set this up so that I can solve it.

Thanks for any help!

Last edited:
To find maximum height, remember that the vertical component of velocity at the maximum height is zero.

Does this help?

Hint: Try using the formulae;

$$v_{f}^{2}=v_{i}^{2}+2ax$$

Edit: Beaten to it.

Whoops! Should post here to let you know I used your hints to figure it out, so thanks!

## 1. What is a "projectile launch point problem"?

A projectile launch point problem is a type of physics problem that involves calculating the initial position and velocity of a projectile in order to predict its trajectory. This type of problem often involves factors such as gravity, air resistance, and the angle of launch.

## 2. Why is it important to solve projectile launch point problems?

Projectile launch point problems are important because they allow us to accurately predict the motion of objects that are launched into the air. This information can be useful in many real-world applications, such as designing projectiles for sports or military use.

## 3. What are the key equations used to solve projectile launch point problems?

The key equations used to solve projectile launch point problems are the equations for projectile motion, which include the equations for displacement, velocity, and acceleration in both the horizontal and vertical directions. These equations take into account the initial position and velocity of the projectile, as well as the effects of gravity and air resistance.

## 4. How can you determine the optimal launch angle for a projectile?

The optimal launch angle for a projectile can be determined by calculating the angle that will give the maximum range or height for the projectile. This can be done by setting up and solving equations for the horizontal and vertical components of velocity, and then using trigonometric functions to find the launch angle that will result in the desired outcome.

## 5. What are some common mistakes when solving projectile launch point problems?

Some common mistakes when solving projectile launch point problems include forgetting to account for the effects of air resistance, using incorrect units for measurements, and not properly setting up or solving the equations for projectile motion. It is important to carefully read and understand the problem, and to double-check calculations to avoid these types of mistakes.

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