Question

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

Answer 1

The sound travels 16.5 meters with a speed of 340 m/s. This means that the sound takes 0.0485 seconds to travel back to you. You hear the sound 2.5 seconds after releasing the ball, so the ball hits the pins at 2.5-0.0485 = 2.45 seconds after release.

Answer 2

i do not understand why you need to know the time that the sound of the ball hitting the pins needs to be known.

Answer 3

omg. the answer is not asking for the time it is asking for the speed of the ball

Answer 4

nvm i got it

Answer 5

To do a problem like this, we have to set up two equations side by side. The first one will be for the sound, and the second for the bowling ball. Lets start by listing the things we know for the sound: Original Position: We will call this 0m, Final Position: 16.5m, Acceleration: 0m/s², Velocity: 340m/s, and time: (2.5-x)--> the x represents the time it takes for the bowling ball to reach the pins (not including travel time of sound), so if we subtract it from the total time (2.5s) then that is equal to the travel time of the sound. Using the equation X= ½at²+V₀t+X₀, where X=final position, a= acceleration, t= time, and X₀ equals original position, we can calculate the actual travel time of the sound. X= ½at²+V₀t+X₀
16.5=½(0)(2.5-x)²+(340)(2.5-x)+0
In this portion of the equation, ½(0)(2.5-x)², the 0 acceleration makes it cancel out. That leaves us with:
16.5=(340)(2.5-x)
16.5=850-340x
-833.5=-340x
x=2.4515 -->This is the t it takes for the bowling ball to reach the pins, excluding sound

We now begin the second half of the problem, concerning the bowling ball. Lets begin by listing what we know about the bowling ball: Original Position: We will call this 0m again, Final Position: 16.5m, Acceleration: 0m/s², Velocity: unknown, and time: 2.4515s. Using the same formula, we plug in these values to find the velocity (speed and velocity are the same thing in this problem because there is only one direction):
X= ½at²+V₀t+X₀
16.5=½(0)(2.4515)²+V₀(2.4515)+0
16.5=V₀(2.4515)
V₀=6.73057m/s

The velocity, or speed in this case, of the bowling ball is 6.73m/s

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