Calculating Range: Zero Air Resistance, Baseball

[1irishman]

Homework Statement

zero air resistance. baseball player hits ball at angle theta above the horizontal at a initial velocity of "z" m/s...how does one calculate range and max height given the fact that the ball lands several metres above where it was originally hit?

Homework Equations

d= vit + 1/2at^2 i think?

The Attempt at a Solution

i need a hint or two please?

 

[gamer_x_]

three hints:

-in which axis is "range" measured?
-what forces do you have acting in this axis?
-based on these forces, formulate your acceleration and displacement equations.

 

[tomcue]

To calculate the range and maximum height of the baseball, we can use the equations for projectile motion. Since there is no air resistance, the only force acting on the ball is gravity. Therefore, the equations we will use are:

- Horizontal displacement: d = v0x * t, where v0x is the initial velocity in the horizontal direction and t is the time.
- Vertical displacement: d = v0y * t + 1/2 * g * t^2, where v0y is the initial velocity in the vertical direction, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
- Maximum height: h = (v0y)^2 / 2g, which is the vertical displacement at the peak of the ball's trajectory.

To calculate the range, we need to first find the time it takes for the ball to reach the ground. This can be done by setting the vertical displacement to 0 and solving for t. Once we have the time, we can plug it into the first equation to find the range.

To calculate the maximum height, we can use the third equation listed above.

Remember to use the initial velocity in both the horizontal and vertical directions when plugging in values for v0x and v0y.

I hope this helps!