Finding initial velocity given max height and distance only

In summary, a golfer hits a ball with a maximum height of 20 m and it lands 130 m away at the same level. The angle was found to be 31.6°, but there is difficulty in solving for the initial velocity using the given equation. Help is needed to find a simpler solution.
  • #1
dane811
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Homework Statement



A golfer hits a ball, giving it a maximum height of 20 m. If the ball lands 130 m away at the level from which he hit it, what was its initial velocity? (Neglect air resistance)

Homework Equations





The Attempt at a Solution



I found the angle to be 31.6, so I tried vi cos 31.6 = 130 /(1/2)((-vi sin 31.6)/-9.81), but I'm not seeing how to solve for initial velocity. There has to be an easier way to do this, and I'm convinced I'm making it more complicated than it really is!

Any help would be appreciated!
 
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  • #2
How do you get the angle to be 31.6°?
 

1. What is the formula for finding initial velocity when given max height and distance only?

The formula for finding initial velocity when given max height and distance only is v0 = √(2gh), where v0 is the initial velocity, g is the acceleration due to gravity (9.8 m/s2), and h is the max height.

2. Can initial velocity be negative when finding it using max height and distance only?

Yes, initial velocity can be negative when finding it using max height and distance only. This indicates that the object was launched downwards instead of upwards.

3. Is the distance traveled in the formula for finding initial velocity the same as the horizontal distance?

No, the distance traveled in the formula for finding initial velocity is the total distance traveled, which includes both the horizontal and vertical components. The horizontal distance is only a part of the total distance traveled.

4. Can the formula for finding initial velocity be used for any object regardless of its mass?

Yes, the formula for finding initial velocity can be used for any object regardless of its mass, as long as the object is only affected by gravity and there are no other external forces acting on it.

5. Is it possible to find the initial velocity if only the max height is known?

Yes, it is possible to find the initial velocity if only the max height is known. However, an additional piece of information, such as the time of flight, is needed to solve for the initial velocity. The formula for finding the initial velocity using max height and time of flight is v0 = h/t, where v0 is the initial velocity, h is the max height, and t is the time of flight.

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