Steep and shallow trajectories

Homework Statement

A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.

Homework Equations

The equations of motion.

The Attempt at a Solution

I realise that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.

Interesting problem.

What I'd do is set up a system of equations. You know that the time it takes for the ball the fall and the time it takes for the ball to travel 5 m is the same, right? So, build two position equations and solve for t, then set them equal to each other, leaving only one variable, your angle.

Keeping the angle as a variable, theta, can you come up with two functions, one for the y position and one for the x position? What should the values of these functions as a whole be for each one?

What part of the 10 m/s is horizontal? Which part of the 10 m/s is vertical?

What I don't understand is how to split to 10m/s into hortizontal and vertical componants in order to get the time.

10 meters per second is the magnitude of the vector. Its the same concept as the hypotenuse of a triangle.

berkeman
Mentor

Homework Statement

A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.

Homework Equations

The equations of motion.

The Attempt at a Solution

I realise that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.

What I don't understand is how to split to 10m/s into hortizontal and vertical componants in order to get the time.

See the "Range and Height" figure at this introductory page:

http://en.wikipedia.org/wiki/Trajectory

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