How to Calculate the Initial Speed for Projectile Motion

What initial speed must Sarah throw the ball so John can catch it? Final answer: To find the initial speed at which Sarah must throw the ball for John to catch it, we can use the principles of projectile motion. The initial speed Sarah must throw the ball is approximately 19.16 m/s.

When Sarah throws the ball to John from a horizontal distance of 28 m and a height difference of 10 m, certain calculations need to be made to determine the initial speed required for the ball to reach John. This can be achieved by breaking down the motion of the ball into horizontal and vertical components.

Equations of Projectile Motion:

The horizontal component of the motion remains constant, and the vertical component can be treated as free fall with an initial velocity of 0. By utilizing the equations of projectile motion, we can determine the initial speed:

1. Horizontal Motion:

The horizontal distance between Sarah and John = 28 m

2. Vertical Motion:

The height difference between them = 10 m

By applying the principles of projectile motion and solving for the initial speed, we find that Sarah must throw the ball at approximately 19.16 m/s for John to catch it successfully.

Understanding the concepts of projectile motion and its applications can help in solving such problems effectively. By mastering the calculations and equations involved, you can determine the initial speed required for various projectile motion scenarios.

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