# Findi angular range given initial velocity and distance

• Niriz
In summary: I've been trying to simplify the equation on the right but I keep getting a quadratic equation. Could someone please help me out with this?In summary, the kicker must kick the ball within an angular range of 20 to 30 degrees in order to score.
Niriz

## Homework Statement

A kicker is attempting a field goal from 50 m from the goal posts, which are 3.44 m high. He can kick the ball with initial speeds of 25 m/s. Ignoring air resistance, within what angular range must he kick the ball to score?

## Homework Equations

Pf = Pi + Fnet*t
And any equations which can be derived from this (the kinematics formula)

## The Attempt at a Solution

I've tried several approaches to this question but none of them seem to be able to neatly isolate one trigonometric function with a number. However I have come up with a few statements that I think should be true:

25m/s = (Vy^ + Vx^)^(1/2) since the components must equal 25 m,

And we know that Vy = sinθ*25 m/s while Vx = cosθ*25 m/s

The time it takes for the ball to reach the goalpost should equal 2/cosθ s, since it must travel 50 metres at a velocity of cosθ*25m/s.

For minimum angle I was thinking that, in time t, the vertical distance it travels must be 3.44 m, so I used the formula d = vi*t + (1/2)at^, so

3.44 m = sinθ*25*(2/cosθ) + 0.5(-9.8m/s^)(2/cosθ)^

But this does not turn simplify into a very nice formula... And is it right of me to think this? One of the biggest issues I'm having is not being able to produce a number for any velocity, because it could be any range of time or distance before Vfy = 0...

Any push in the right direction would be greatly appreciated! Such as another relationship equation...

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Also, the minimum angle should be at the point where the displacement vector of the ball is (50, 3.44, 0), since any more and the angle could be lower, and any less y displacement it wouldn't go over the post..

Bumping again!

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## 1. How do you calculate the angular range given the initial velocity and distance?

To calculate the angular range, you can use the formula θ = sin^-1 (d/g(v^2 + (d tanθ)/g)), where θ is the angular range, d is the distance, v is the initial velocity, and g is the acceleration due to gravity. This formula assumes no air resistance and a flat surface.

## 2. What is the significance of finding the angular range?

The angular range is important because it tells us the maximum angle at which an object can be launched in order to reach a certain distance with a given initial velocity. This is useful in a variety of applications, such as sports, engineering, and physics experiments.

## 3. Can the angular range be negative?

No, the angular range cannot be negative. It represents an angle, and angles cannot be negative. If you get a negative value when calculating the angular range, it means that the object cannot reach the desired distance with the given initial velocity.

## 4. How does air resistance affect the calculation of angular range?

Air resistance can significantly affect the calculation of the angular range. The formula mentioned in the first question assumes no air resistance, so it may not accurately predict the actual angular range. In real-life situations, air resistance must be taken into account for a more accurate calculation.

## 5. Are there any limitations to using the formula for calculating angular range?

Yes, there are some limitations to using the formula. It assumes a flat surface and no air resistance, which may not always be the case in real-life situations. Additionally, the formula may not accurately predict the angular range for objects with complex shapes or irregular trajectories.

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