Calculating Passing Height of Two Thrown Balls

In summary, Ball A and Ball B are thrown vertically with speeds of 40 m/s and 47.5 m/s respectively. The question asks for the height at which the two balls will pass each other, assuming a gravitational acceleration of 10m/s2. By using the equations s = vt + ½at2 and t = v/g, we can solve for the time it takes Ball A to reach its maximum height (4 seconds) and determine that Ball B is thrown 1 second later. To find the height at which the two balls pass each other, we can set up a kinematics equation for each ball and solve for the height at which they are the same distance above the ground.
  • #1
Said Ahmad
8
1

Homework Statement



Ball A is thrown vertically by speed 40 m/s. After 1 second, Ball B is thrown vertically also by speed 47.5 m/s.
What height from ground will they pass each other? ( g = 10m/s2 )

Homework Equations



s = vt + ½at2
t = v/g
v2 = v02 + 2as

The Attempt at a Solution



Time A to reach the max height is t = v/g = 40/10 = 4 s

I don't understand. Because there is plus of 1 sec for ball B.
 
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  • #2
Said Ahmad said:

Homework Statement



Ball A is thrown vertically by speed 40 m/s. After 1 second, Ball B is thrown vertically also by speed 47.5 m/s.
What height from ground will they pass each other? ( g = 10m/s2 )

Homework Equations



s = vt + ½at2
t = v/g
v2 = v02 + 2as

The Attempt at a Solution



Time A to reach the max height is t = v/g = 40/10 = 4 s

I don't understand. Because there is plus of 1 sec for ball B.
What's not to understand?

Both balls are thrown up in the same direction, although at different times and different speeds. The two balls are going to pass each other at some point, either on the way up or on the way down. At what height are the two balls the same distance above the ground?

Hint: write a kinematics equation for each ball.
 

1. How do you calculate the passing height of two thrown balls?

The passing height of two thrown balls can be calculated by using the formula: H = (V1^2 sin^2θ)/(2g), where H is the passing height, V1 is the initial velocity of the first ball, θ is the angle at which the balls are thrown, and g is the acceleration due to gravity.

2. What is the importance of calculating the passing height of two thrown balls?

Calculating the passing height of two thrown balls is important in understanding and predicting the trajectory and motion of the balls. It can also be useful in sports such as baseball and softball, where players need to anticipate and catch or hit a thrown ball at a certain height.

3. How does the initial velocity of the balls affect the passing height?

The initial velocity of the balls is a key factor in determining the passing height. The higher the initial velocity, the higher the passing height will be. This is because the balls will travel further and stay in the air for a longer time.

4. Can the passing height of two thrown balls change during flight?

Yes, the passing height of two thrown balls can change during flight due to factors such as air resistance, wind, and changes in the initial velocity or angle of the balls. However, the formula for calculating the passing height assumes no external forces acting on the balls.

5. How can the angle at which the balls are thrown affect the passing height?

The angle at which the balls are thrown can greatly affect the passing height. A higher initial angle will result in a higher passing height, while a lower initial angle will result in a lower passing height. This is because the angle determines the vertical component of the initial velocity, which is a major factor in determining the height of the balls' trajectory.

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