# A ball, thrown at a 39 degree angle, Intial X and Y velocity not given

• MRGE
In summary, a ball thrown from a 200 meter high cliff at an angle of 49 degrees travels a distance of 400 meters before coming to a stop. Its initial speed is somewhere between 50 and 55 m/s.
MRGE

## Homework Statement

A ball thrown from a 200 meter high cliff at an angle of 49 degrees. The ball traveled a distance of 400 meters from the base of the cliff. Find the Initial Speed of the ball.

O - Ball
I
I
I - Cliff 200 meters
I
I
I
I
............
Distance traveled 400 meters.

## The Attempt at a Solution

I couldn't figure out how I can find the velocity at all. I tried the time between 200 meters for the ball to fall down and factor it in but didn't get it. Somehow, I would need to find the time or at least the maximum height of the ball. Hints would be great.

The trick on all these trajectory problems is to separate the initial velocity into horizontal and vertical components using trigonometry. Then make two headings, horizontal and vertical.
Under horizontal you have uniform motion (no acceleration) so you put d = vt.
Under vertical you have the acceleration of gravity, so you put
V = Vo + at and X = Xo + Vo*t + .5*a*t^2

Fill in the initial velocities and anything else you know in all three formulas. Usually you can solve one of them to find the time or something. If not, use two of them as a system of equations with 2 unknowns.

i tried that but there are still two variables left. The Time and Velocity of X and Y.

All that was given is the height at which the ball was thrown from, the angle it was thrown and how far it went. I can't figure out the max height to get the time of the duration or the velocities. Anyone have a solution?

MRGE said:
i tried that but there are still two variables left. The Time and Velocity of X and Y.

All that was given is the height at which the ball was thrown from, the angle it was thrown and how far it went. I can't figure out the max height to get the time of the duration or the velocities. Anyone have a solution?

Well, you have 2 variables ... but you also have 2 equations given by Delphi.

Fill in the values of sin39 and cos39 and simply grind it out.

MRGE said:

## Homework Statement

A ball thrown from a 200 meter high cliff at an angle of 49 degrees. The ball traveled a distance of 400 meters from the base of the cliff. Find the Initial Speed of the ball.

O - Ball
I
I
I - Cliff 200 meters
I
I
I
I
............
Distance traveled 400 meters.

## The Attempt at a Solution

I couldn't figure out how I can find the velocity at all. I tried the time between 200 meters for the ball to fall down and factor it in but didn't get it. Somehow, I would need to find the time or at least the maximum height of the ball. Hints would be great.

1. The ball would need to be thrown faster than any human can actually throw a ball, especially since it's thrown at a 49 degree angle above horizontal, but we'll assume someone mighty enough can actually achieve such throwing velocities.

2. Launch velocity hint: I know precisely what the ball's initial launch velocity is, but I won't spoil it for you. It's somewhere between 50 and 55 m/s.

## 1. What is the initial velocity of the ball?

The initial velocity of the ball cannot be determined without knowing the values of the X and Y components of the velocity.

## 2. How far will the ball travel?

The distance the ball will travel depends on the initial velocity, angle of projection, and the effects of air resistance. Without knowing the initial velocity, it is impossible to accurately determine the distance the ball will travel.

## 3. What is the maximum height the ball will reach?

The maximum height the ball will reach also depends on the initial velocity and angle of projection. Without these values, the maximum height cannot be calculated.

## 4. How long will the ball be in the air?

The time the ball will be in the air is dependent on the initial velocity and angle of projection. Without these values, it is not possible to accurately determine the time the ball will be in the air.

## 5. What is the trajectory of the ball?

The trajectory of the ball is determined by the initial velocity, angle of projection, and the effects of air resistance. Without knowing the initial velocity, the trajectory cannot be accurately determined.

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