A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 15.5 m long. The bowler hears the sound of the ball hitting the pins 2.50 s after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m/s.

How do i do this problem as well as the following one as well?

A tortoise can run with a speed of 16.0 cm/s, and a hare can run exactly 25 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.00 min. The tortoise wins by 20.0 cm.(a) How long does the race take?(b) What is the length of the race?

t = 2.5 s - 15.5 m / 340 m/s,

= 2.5 - 0.0456 = 2.454 s.

d = Vt,
15.5 = V*2.454,
V = 15.5 / 2.454 = 6.33 m/s.

16/.20 = 80

80x25=2000cm distance

t=2000/16 = 125s

see you in Bentleys class :]

To solve both of these problems, we can use the formula:

Distance = Speed x Time

Let's start with the first problem about the bowling ball.

Given:
- Length of the bowling lane (Distance) = 15.5 m
- Time taken for the sound to reach the bowler's ears (Time) = 2.50 s
- Speed of sound (Speed) = 340 m/s

We can use the formula to find the time it took for the ball to reach the pins:

Distance = Speed x Time

15.5 m = Speed x 2.50 s

Divide both sides of the equation by 2.50 s to solve for Speed:

Speed = 15.5 m / 2.50 s ≈ 6.2 m/s

So, the speed of the bowling ball is approximately 6.2 m/s.

Now let's move on to the second problem about the race between the tortoise and the hare.

Given:
- Speed of the tortoise = 16.0 cm/s
- Speed of the hare = 25 times the speed of the tortoise = 25 x 16.0 cm/s = 400 cm/s
- Winning distance of the tortoise = 20.0 cm
- Hare stops to rest for 2.00 min (convert to seconds)

(a) To find the time it takes for the tortoise to win the race:

Let's assume the time taken by both the tortoise and the hare is "t" seconds.

The distance travelled by the tortoise in "t" seconds is:

Distance = Speed x Time = 16.0 cm/s x t

The distance travelled by the hare in "t" seconds is:

Distance = Speed x Time = 400 cm/s x t

Since the tortoise wins the race by a distance of 20.0 cm, we can set up the following equation:

16.0 cm/s x t = 400 cm/s x t + 20.0 cm

Simplify the equation:

20.0 cm = 384.0 cm/s x t

Divide both sides of the equation by 384.0 cm/s to find t:

t = 20.0 cm / 384.0 cm/s ≈ 0.0521 s

So, the race takes approximately 0.0521 seconds.

(b) To find the length of the race:

The distance travelled by the tortoise in "t" seconds is:

Distance = Speed x Time = 16.0 cm/s x t

Using the value of t we found earlier:

Distance = 16.0 cm/s x 0.0521 s ≈ 0.8352 cm

So, the length of the race is approximately 0.8352 cm