A ball is shot from the ground into the air and horizontal distance

[cnalamolu]

1. The problem statement, all variables and given/known da
A ball is shot from the ground into the air. At a height of 9.7 m, the velocity is observed to be
v = (7.4)i + (5.1)j in meters per second (i horizontal, j upward).

Homework Equations

What will be the total horizontal distance traveled by the ball?
What is the velocity of the ball (magnitude and direction) the instant before it hits the ground? What is its j-component?

The Attempt at a Solution

I have no idea please help!

 

[jhae2.718]

Are you familiar with the kinematic equations for projectile motion?

 

[cnalamolu]

yes please explain.

 

[jhae2.718]

The basic equations of motion for a projectile with no air resistance are:
$$x(t)=v_{0x}t$$
$$y(t)=v_{0y}t-\frac{gt^2}{2}$$
This assumes the projectile starts from (0,0), which is hinted at in the problem. Here, $$v_{0x}$$ is the x-component of initial velocity, and $$v_{0y}$$ is the y-component of initial velocity.

Now, what are your knowns and unknowns? Before you can use these equations to find the "wants", you need to solve for some of the values of the equations. (Hint: you'll need another equation that relates velocity, position, and acceleration to find the initial velocity. Also, take into account the fact that in the x direction there is no acceleration, so what happens to the x velocity over time?)