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

[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.

Homework Equations

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.

 

[Delphi51]

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.

 

[MRGE]

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?

 

[LowlyPion]

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.

 

[Gnosis]

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.

Homework Equations

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.