Solving Projectile Motion Equations for Initial Velocity and Angle

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Homework Help Overview

The problem involves projectile motion, specifically analyzing the motion of a ball thrown horizontally from a height of 20 meters. The objective is to determine the initial velocity and the angle at which the ball strikes the ground, given that it hits the ground with a speed of 3u.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss separating the horizontal and vertical components of motion. One participant calculates the final vertical velocity and considers the relationship between the components to form a triangle, questioning if this approach is correct.

Discussion Status

There is an ongoing exploration of the relationships between the components of motion. Some guidance has been offered regarding the use of Pythagoras to relate the components, but no consensus has been reached on the next steps or final values.

Contextual Notes

Participants are working under the constraints of the problem statement and the equations of motion, with some uncertainty about the next steps to find the initial velocity.

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Homework Statement


A ball is thrown horizontally with speed u from a height of 20m. It hits the ground with a speed 3u. Find the value of u, and the angle at which the ball strikes the ground.


Homework Equations


The equations of motion.

The Attempt at a Solution


I know that I must deal separately with the horizontal and vertical components of the motion.
I have worked out that the final vertical velocity will be 19.8m/s but I don't where to go next to find u.
 
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Write an expression for the speed at which it hits the ground. Set it equal to the required condition.
 
I have realized that I now have a triangle where the x component is u, y component is 19.8 and the hypotenuse is 3u. So I could easily work out u and then the angle by using simple trig.

Is this correct?
 
Looks good! Perhaps consider using Pythagoras.
 

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