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 2.44 s after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m/s.
See previous post: Mon, 9-28-15, 9:46 PM
To find the speed of the ball, we can use the formula:
Speed = Distance / Time
First, let's calculate the time it takes for the ball to reach the pins. We know that the length of the bowling lane is 16.5 m and the speed of the ball is constant. Therefore, we can use the formula:
Time = Distance / Speed
Time = 16.5 m / Speed
Next, we are given that the bowler hears the sound of the ball hitting the pins 2.44 seconds after the ball is released from his hands. This is the total time it takes for the ball to travel the distance of the lane plus the time it takes for the sound to reach the bowler. So, we have:
Total time = Time + Time for sound
2.44 s = (16.5 m / Speed) + (16.5 m / 340 m/s)
Now we can solve for Speed. Rearranging the equation, we get:
2.44 s - (16.5 m / 340 m/s) = 16.5 m / Speed
To simplify the equation, let's convert the unit of seconds to milliseconds:
2.44 s = 2440 ms
Substituting the values, we have:
2440 ms - (16.5 m / 340 m/s) = 16.5 m / Speed
Now, let's solve for Speed.
Speed = 16.5 m / (2440 ms - (16.5 m / 340 m/s))
Speed = 16.5 m / (2440 ms - 0.0485 s)
Speed = 16.5 m / 2.3915 s
Speed = 6.89295 m/s
Therefore, the speed of the ball is approximately 6.89 m/s.