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 2.51s after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m/s

Speed of ball is distance traveled divided by (time of hearing minus time the sound travels).

16.5/(2.51-16.5/340) m/s = 6.70 m/s

To find the speed of the ball, we can use the equation:

Speed = Distance / Time

Given:
Distance = 16.5 m
Time = 2.51s

Plugging these values into the equation, we get:

Speed = 16.5 m / 2.51s

Simplifying, we find:

Speed = 6.575 m/s

Therefore, the speed of the ball is approximately 6.575 m/s.

To solve this problem, we need to consider the time it takes for the sound to reach the bowler after the ball hits the pins. We know the speed of sound is 340 m/s.

First, let's calculate the time it takes for the ball to reach the pins. We know the distance the ball travels is 16.5 m, and we want to find the time it takes for the ball to travel that distance.

Using the formula:

Distance = Speed × Time

We can rearrange the formula to solve for time:

Time = Distance / Speed

Plugging in the values:

Time = 16.5 m / Speed

Now, let's calculate the time it takes for the sound to travel back to the bowler. We know the time is 2.51 seconds.

The total time is the time it takes for the ball to reach the pins plus the time it takes for the sound to travel back:

Total time = Time taken for ball to reach pins + Time taken for sound to travel back

Total time = 2.51 s

We know that the speed of sound is 340 m/s. Rearranging the formula, we can solve for the time taken for the sound to travel back:

Time taken for sound to travel back = Distance / Speed

Since the sound has to travel twice the distance (forward and backward), we can substitute 2 x Distance:

2 x Distance / Speed = 2 x (16.5 m) / 340 m/s

Now, let's substitute the values into the equation:

2 x (16.5 m) / 340 m/s = 2 x 16.5 / 340 = 0.0971 s

Now we can calculate the time it takes for the ball to reach the pins:

Total time - Time taken for sound to travel back = Time taken for ball to reach pins

2.51 s - 0.0971 s = 2.4129 s

Now, let's equate the two times. Since the time for the ball to reach the pins equals the time for the ball to travel the distance:

16.5 m / Speed = 2.4129 s

Now we can solve for the speed:

Speed = Distance / Time

Speed = 16.5 m / 2.4129 s = 6.833 m/s

Therefore, the speed of the ball is 6.833 m/s.

time=time for ball to roll+timefor sound to come back.

2.51=speedball(2.51-tsound)+tsound

but tsound=16.5/340

solve for speedof ball