How Do You Calculate Initial Speed in Projectile Motion Problems?

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To calculate initial speed in projectile motion, one must consider both horizontal and vertical components of motion. In the first problem, a ball thrown horizontally from 22 m hits the ground with a speed three times its initial speed, while the second problem involves a projectile fired at a 30° angle from 41 m, striking the ground at 1.4 times its initial speed. The user attempted to apply the kinematic equation V^2=Vo^2+2ah but encountered errors, suggesting the need for a clearer understanding of vertical acceleration. It is emphasized that only the vertical component of motion is subject to acceleration due to gravity. Clarifying the calculations and focusing on the vertical motion will lead to the correct initial speed.
heeling23
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1. A ball is thrown horizontally from a height of 22 m and hits the ground with a speed that is three times its initial speed. What was the initial speed?

2. A projectile is fired with initial speed v at an angle 30° above the horizontal from a height of 41 m above the ground. The projectile strikes the ground with a speed of 1.4v. Find v.

These are essentially the same problems right? Except for the fact that #2 has a vertical initial velocity. I tried using V^2=Vo^2+2ah but I got the answer wrong. Then I tried finding the time for the first one using y=1/2at^2 and then using v=vo+at and I got the wrong answer again.

Any help is appreciated!
Thanks,
heeling23
 
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heeling23 said:
I tried using V^2=Vo^2+2ah but I got the answer wrong. Then I tried finding the time for the first one using y=1/2at^2 and then using v=vo+at and I got the wrong answer again.
Either approach, done correctly, would work. Post the details of what you did for more help. (Hint: Only the vertical component of motion is accelerated.)
 
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