# Determine the ratio of the times for the one-bounce and no-bounce throws

• Sunnie
In summary, the conversation discussed the technique of allowing a baseball to bounce before reaching the infield and the relationship between the angle of the throw and the ball's speed after the bounce. The conversation also asked for help in determining the angle and ratio of times for a one-bounce throw to match the distance of a no-bounce throw. A formula was also requested for computing the flight time and distance without bounces given the initial speed and angle.
Sunnie
When baseball players throw the ball in from the outfield, they usually allow it to take one bounce before it reaches the infield, on the theory the ball arrives sooner that way. Suppose the angle at which a bounced ball leaves the ground is the same as the angle at which the outfielder threw it, as in the figure, but that the ball's speed after the bounce is one half of what it was before the bounce.

(a) Assuming the ball is always thrown with the same initial speed, at what angle should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 40.0° with no bounce (green path)?
°

(b) Determine the ratio of the times for the one-bounce and no-bounce throws.
(one-bounce time / no-bounce time)

Does anyone know how to do this problem. I have no formula's for this does anyone now the formula's?

do you know how to compute the flight time and distance without bounces with a given initial speed an angle?

I can provide a response to this content. To determine the ratio of the times for the one-bounce and no-bounce throws, we first need to understand the concept of projectile motion. When an object, such as a baseball, is thrown at an angle, it follows a curved path known as a parabola. The time it takes for the object to reach the ground is determined by its initial velocity, angle of projection, and the acceleration due to gravity.

In this scenario, we are given that the angle of projection for both the one-bounce and no-bounce throws is the same. However, the speed of the ball after the bounce is one half of its initial speed. This means that the time it takes for the ball to reach the ground after the bounce will also be half of the time it takes for the ball to reach the ground without bouncing.

To answer part (a) of the question, we can use the formula for the range of a projectile, which is given by R = (v^2 * sin2θ)/g, where R is the range, v is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. Since we are looking for the same distance D for both the one-bounce and no-bounce throws, we can set the ranges equal to each other and solve for the angle θ.

R(one-bounce) = R(no-bounce)
(v^2 * sin2θ)/g = (v^2 * sin40)/g
sin2θ = sin40
2θ = 40
θ = 20 degrees

Therefore, the angle at which the fielder should throw the ball is 20 degrees.

To answer part (b) of the question, we can use the formula for the time of flight of a projectile, which is given by t = (2v * sinθ)/g, where t is the time of flight. Since we know the initial velocity and angle of projection for both throws, we can calculate the time for each throw.

t(one-bounce) = (2 * v/2 * sin20)/g = (v * sin20)/g
t(no-bounce) = (2 * v * sin40)/g

The ratio of the times for the one-bounce and no-bounce throws is given by:
t(one-bounce)/t(no-bounce) = [(v * sin

## 1. What is the purpose of determining the ratio of the times for one-bounce and no-bounce throws?

The purpose of determining this ratio is to understand the difference in time it takes for an object to travel a certain distance when it bounces compared to when it does not bounce. This can provide insight into the energy transfer and efficiency of the throwing motion.

## 2. How do you measure the times for one-bounce and no-bounce throws?

To measure the time, you can use a stopwatch or a high-speed camera to record the time it takes for the object to travel a certain distance. For more accurate results, multiple trials should be conducted and the average time should be calculated.

## 3. What factors can affect the ratio of the times for one-bounce and no-bounce throws?

The ratio can be affected by factors such as the force and angle of the throw, the weight and shape of the object, air resistance, and the surface it bounces on. These factors can impact the energy transfer and the path of the object, leading to different times for one-bounce and no-bounce throws.

## 4. How can determining this ratio be useful in sports or other applications?

In sports such as basketball or tennis, understanding this ratio can help improve the throwing technique and increase the chances of a successful throw. It can also be useful in other applications such as designing equipment for throwing or predicting the trajectory of projectiles.

## 5. Are there any limitations to using this ratio to analyze throwing motion?

Yes, there are limitations as this ratio only considers the time taken for the object to travel a certain distance. It does not take into account factors such as accuracy, consistency, or the overall success of the throw. Other measures and techniques may need to be used in conjunction with this ratio to fully analyze throwing motion.

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