Solving Projectile Motion Equations for Initial Velocity and Angle

AI Thread Summary
A ball is thrown horizontally from a height of 20m with an initial speed u and impacts the ground at a speed of 3u. The vertical component of the final velocity is calculated to be 19.8 m/s. To find the initial speed u, the relationship between the horizontal and vertical components can be established using trigonometry, forming a right triangle where the x component is u, the y component is 19.8 m/s, and the hypotenuse is 3u. The discussion suggests using the Pythagorean theorem to solve for u and subsequently determine the angle of impact. The approach is confirmed as correct and effective for solving the problem.
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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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