# Finding Initial Velocity to Solve Bowling Ball Speed Problem

• danosu43
In summary, the problem involves finding the speed of a bowling ball that travels with constant velocity and hits pins at the end of a 16.5 m long bowling lane. The bowler hears the sound of the ball hitting the pins 2.45s after it is released. Using the speed of sound and the time it took for the sound to return, the velocity of the ball can be calculated to be approximately 6.87 m/s.
danosu43
I've tried a few different equations but I'm not sure how to start this problem. I just realized I'm looking for the initial velocity since the speed of the ball is constant.

A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears the sound of the ball hitting the pins 2.45s after the ball is released from his hands. What is the speed of the ball?

Speed of sound=340 m/s
Bowling lane=16.5 m
Time till sound of ball heard=2.45s

This where I'm confused because I'm not sure which equations are the right ones to use.

Here is what I've attempted so far and I think I just realized its all wrong:

v=v(initial)+at
340 m/s=0+a(2.5s)
a=136m/s^2

(16.5m)/(2.45s)=6.73 s

I'm pretty sure this work is wrong but any help to start in the right direction would be much appreciated.

The problem states that the ball is traveling at constant velocity so acceleration is not an issue. Knowing the speed of sound, figure out how long it took for the ball to hit the pins. Then knowing the time and distance of the lane you can find the velocity.

If speed of sound=340 m/s then (16.5m)/(340m/s)=0.049s. Subtract that from 2.45s and it took the ball 2.401s to reach the pins and then 0.049s for the sound to return back to the person. Correct?

Then the velocity=16.5m/2.401s which gives v=6.87 m/s

Looks good to me

## 1. What is the formula for finding initial velocity in a bowling ball speed problem?

The formula for finding initial velocity in a bowling ball speed problem is v = √(g*d/sin(2θ)), where v is the initial velocity, g is the acceleration due to gravity (9.8 m/s²), d is the distance the ball travels, and θ is the launch angle.

## 2. How do I determine the launch angle in a bowling ball speed problem?

The launch angle can be determined by measuring the angle at which the ball is released from the hand. This can be done using a protractor or by estimating the angle visually.

## 3. What is the value of acceleration due to gravity used in the formula?

The value of acceleration due to gravity used in the formula is 9.8 m/s². This is a constant value and is the same for all objects near the surface of the Earth.

## 4. Can I use a different unit for distance in the formula?

Yes, you can use a different unit for distance in the formula as long as it is consistent with the units used for acceleration due to gravity and initial velocity. For example, if you use meters (m) for acceleration and initial velocity, you should also use meters for distance.

## 5. Is it necessary to know the mass of the bowling ball to find the initial velocity?

No, it is not necessary to know the mass of the bowling ball to find the initial velocity. The formula for finding initial velocity in a bowling ball speed problem does not include the mass of the ball. However, the mass of the ball can affect the speed and distance it travels due to factors such as air resistance and friction.

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