How Do You Calculate Maximum Height in Projectile Motion Using Calculus?

In summary, the conversation is about a person needing help with two questions regarding shooting a paper clip into the air on Earth and the moon. They want to know the time and maximum height the clip will reach. The expert suggests finding the maximum height by finding the zero of the derivative of the function and solving for t. They also clarify that the clip will be shot up at 64 feet per second and not necessarily reach a height of 64 feet in the air. The expert then asks the person to show their solution so they can check it.
  • #1
orangesang
2
0
Ok.
So I need two questions answered so i can check answers with what u guys got.


1. a. On Earth, you could easily shoot a paper clip 64 feet straight up into the air with a rubber band. After t seconds, the clip will be H(t)= 64t-16t^2 feet above you.

How long will it take the clip to reach its maximum height?

b. On the moon, an identical launch would send the clip to a height of H(t)=64t-2.6t^2

How long would it take for the clip to reach its maximum height and what would be that height?


Ok. So if you could show me how you did it also it would really help.
 
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  • #2
The t value of the maximum will be a zero of H'(t) since that is when the paper clip stops going up and starts to go back down. Since H'(t) = 64-32t, 64-32t=0 => 64=32t => t=2 with H(2) = 64.

Also, you would be shooting the paperclip up at 64 feet per second from a height of 0 feet with that equation, not necessarily up 64 feet in the air.
 
  • #3
orangesang said:
Ok. So if you could show me how you did it also it would really help.

Can you show us how you did it?
 
  • #4
You initially said that you had already solved the problem and just wanted to check your answers.
Now you say you do not know how to do the problem.

How about showing YOUR solution so we can check it?
 

FAQ: How Do You Calculate Maximum Height in Projectile Motion Using Calculus?

What is Calculus and how is it related to projectile motion?

Calculus is a branch of mathematics that deals with the study of change and motion. It is related to projectile motion because it helps us understand the motion of objects in the air, such as a ball being thrown or a rocket being launched.

How is Calculus used in analyzing projectile motion?

Calculus is used to calculate the position, velocity, and acceleration of an object in projectile motion. It helps us understand the relationship between distance, time, and acceleration and allows us to make predictions about the trajectory of a projectile.

What are the key concepts in Calculus that are important for understanding projectile motion?

The key concepts in Calculus that are important for understanding projectile motion include derivatives, integrals, and limits. These concepts help us analyze the rate of change, area under a curve, and the behavior of a function, respectively.

How does air resistance affect projectile motion and how is it accounted for in Calculus?

Air resistance can significantly impact the trajectory of a projectile by slowing it down and altering its path. In Calculus, air resistance is accounted for by using differential equations and considering the force of drag in the equations of motion.

Can Calculus be used to solve real-world problems involving projectile motion?

Yes, Calculus is widely used in solving real-world problems involving projectile motion. It is used in various fields such as physics, engineering, and sports to make predictions and optimize the motion of objects in the air.

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