# Projectile Motion word problem from Calc III course (finding height of a wall).

• jtex316
In summary, the problem is about determining the distance of a 2m-high wall from the launch point of a ball thrown at an initial velocity of 20m/sec and an angle of 60 degrees. The solution involves finding the time it takes for the ball to reach a height of 2m and using that to determine the horizontal distance the ball has traveled. The author's solution assumes that the ball just barely clears the wall.
jtex316
The problem is from the MIT Open CourseWare Calculus eBook by Strang. Chapter 12.2, #3:

A ball is thrown at 60 degrees with initial velocity of 20m/sec to clear a wall 2m high. How far away is the wall?

Finding flight time T, range R, and max height Y(max) is the easy part. How do I find how far away the 2m-high wall is? I understand that this has two solutions (the wall is going to be really close to the launch point, or really close to the end point). How do I calculate the solutions? Please note that it's been a very long time since Physics I.

I've attempted to take the Range and subtract the height of the wall from it, but that doesn't work. I feel like instead of Y(max) I need Y(2m), but I don't know how to do that.

You don't need to work out the problem - a link to an example or a little push is all I'm looking for here.

Thanks!

jtex316 said:
The problem is from the MIT Open CourseWare Calculus eBook by Strang. Chapter 12.2, #3:

A ball is thrown at 60 degrees with initial velocity of 20m/sec to clear a wall 2m high. How far away is the wall?

Finding flight time T, range R, and max height Y(max) is the easy part. How do I find how far away the 2m-high wall is? I understand that this has two solutions (the wall is going to be really close to the launch point, or really close to the end point). How do I calculate the solutions? Please note that it's been a very long time since Physics I.

I've attempted to take the Range and subtract the height of the wall from it, but that doesn't work.
The range is the distance the projectile moves horizontally, right? It doesn't really make sense to subtract a vertical distance from it. Remember that the motion in the horizontal and vertical directions are separate from each other.

I feel like instead of Y(max) I need Y(2m), but I don't know how to do that.
I'm not clear on your notation here. Ymax usually denotes the maximum height the projectile reaches. Y2 m would tautologically be equal to 2 m.

You don't need to work out the problem - a link to an example or a little push is all I'm looking for here.
Start by finding the time it takes for the ball to reach a height of 2 meters.

Hey there, thanks for your reply. Apparently it looks like I'm going to need to see the problem worked out. I have struggled with this, trying to use T, R, and Y(max) formulas and just don't see how to get to the answers as the author has.

The only way you can do this problem is to assume they mean that the ball just barely clears the wall. That is, as vela said, solve for the time it takes the ball to reach a height of 2m. Use that height to determine the horizontal distance the ball has gone.

If you have tried this yourself but don't get the answers the author has, show us what you have done, what answer you got, and what the author's answer is.

## 1. How do I set up the equation for a projectile motion word problem?

The equation for projectile motion is typically set up as h(t) = -16t^2 + v0t + h0, where h(t) is the height of the object at time t, v0 is the initial velocity, and h0 is the initial height. This equation can be derived from the equations for displacement, velocity, and acceleration in the y-direction.

## 2. How do I find the initial velocity in a projectile motion word problem?

The initial velocity can be found by using the equation v0 = √(v0x^2 + v0y^2), where v0x is the initial velocity in the x-direction and v0y is the initial velocity in the y-direction. These values can be determined from the given information in the problem, such as the angle of launch and the magnitude of the initial velocity.

## 3. How do I determine the height of the wall in a projectile motion word problem?

To find the height of the wall, you will need to set up and solve an equation that relates the height of the object at a certain time to the height of the wall. This can be done by finding the time at which the object reaches the wall and plugging that time into the equation for height, h(t).

## 4. How does air resistance affect projectile motion?

Air resistance can affect projectile motion by decreasing the initial velocity and causing the object to slow down more quickly. This can change the trajectory of the object and result in a shorter distance traveled and a lower maximum height.

## 5. What is the difference between horizontal and vertical projectile motion?

Horizontal projectile motion occurs when an object is launched at an angle and moves horizontally, while vertical projectile motion occurs when an object is launched straight up or down. The equations and calculations for these two types of motion are different, but they can also be combined to solve for the overall motion of an object in two dimensions.

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