Solving a Physics Problem: How Far Will the Ball Land?

• luke34
In summary, a batter hits a ball at an angle of 65 degrees with an initial velocity of 30 m/s and 1 meter above the ground. Using the equations X= Vcos65 and Y= Vsin65, the x component was calculated to be 12.68 and the y component to be 27.19. However, the equation X=X(initial) + V(initial x)T + .5A(x)T^2 is only applicable to vertical motion and cannot be used to find the range. Instead, the Y component should be used to find the time and then the range can be calculated using the horizontal component in that time.
luke34
Ok here's the problem:
A batter hits a ball which leaves the bat 1 meter above the ground at an angle of 65 degrees with an initial velocity of 30 m/s. How far from home plate will the ball land if not caught and ignoring any air resistence?

So I tried solving for how much of the velocity is is the x and y components.
X= Vcos65
Y= Vsin65
which gave me x=12.68 and y=27.19

Then using the equation X=X(initial) + V(initial x)T + .5A(x)T^2
I plugged in my numbers to get 0=1+12.68t+.5(9.8)T^2.

This is where I'm stuck. Am I on the right track or what? Help please. Thanks.

That equation is for the vertical motion only, so it won't give you the range, which is what this problem is asking for. It actually doesn't make any sense to use the x component in that way, in that equation.

But this equation would be useful in finding the time it would take to land on the ground after being hit.

Then perhaps you could figure out how far it would travel in the horizontal direction in that time, and that would give you the range.

Dorothy

So what exactely am I suppose to do if I shouldn't use the x componet to solve for time?

Why use the horizontal component of motion in an equation which describes the vertical motion of the object? Use the Y component.

Oh I see. Seems so obvious now. Thanks

1. How do I calculate the distance a ball will travel?

To calculate the distance a ball will travel, you will need to use the formula d = v0t + 1/2at^2, where d is the distance, v0 is the initial velocity, t is the time, and a is the acceleration. You will also need to know the height from which the ball is dropped.

2. What is the initial velocity of the ball?

The initial velocity of the ball is the speed at which the ball is launched or dropped. This can be measured using a speedometer or calculated based on the force applied to the ball and its mass.

3. How does air resistance affect the distance the ball will travel?

Air resistance can decrease the distance a ball will travel by slowing it down. The amount of air resistance depends on the shape and size of the ball, as well as the air density. In some cases, air resistance can be negligible and can be ignored in calculations.

4. Can I use the same formula to calculate the distance for different types of projectiles?

The formula d = v0t + 1/2at^2 can be used to calculate the distance for any type of projectile as long as the initial velocity and acceleration are known. However, for more complex projectiles, such as those with non-uniform acceleration or involving air resistance, the formula may need to be modified.

5. How can I improve the accuracy of my calculations for the distance a ball will land?

To improve the accuracy of your calculations, you can use more precise measurements for the initial velocity, time, and height. You can also take into account external factors such as air resistance and wind. Additionally, performing multiple trials and taking the average can help to reduce errors in the calculation.

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