Physics questions. help!

Question

1) A ball traveling with constant speed hits the pins placed at the end of a bowling lane 16.5 m long. The bowler heard the sound of the ball hitting the pins 2.50 s after the ball was released from his hands. What was the speed of the ball? The speed of sound is 340 m/s.

2) A sports car accelerates from rest to 100 km/h in 6.6 s. What is its acceleration in m/s^2?

3) At highway speeds, a particular automobile is capable of an acceleration of about 1.7 m/s^2. At this rate, how long does it take to accelerate from 85 km/h to 100 km/h?

Answer 1

<< A ball traveling with constant speed hits the pins placed at the end of a bowling lane 16.5 m long. The bowler heard the sound of the ball hitting the pins 2.50 s after the ball was released from his hands. What was the speed of the ball? The speed of sound is 340 m/s.>>

The working formula is

Distance = Rate * Time

Equation 1: 16.5 = VT

Equation 2: 16.5 = 340(2.5 - T)

where

V = speed of the ball

T = time it took for the ball to strike the pins

From Equation 1, T = 16.5/V and substituting this in Equation 2,

16.5 = 340(2.5 - 16.5/V)

16.5 = 850 - 5610/V

Multiplying both sides by V,

16.5V = 850V - 5610

Rearranging the above,

850V - 16.5V = 5610

833.5V = 5610

V = 6.73  m/sec.

<< A sports car accelerates from rest to 100 km/h in 6.6 s. What is its acceleration in m/s^2? >>

acceleration = a = velocity/time

a = (100 km/hr)(1000 m/km)(1 hour/3600 sec) / 6.6 sec

a = 4.21 m/sec^2

<<  At highway speeds, a particular automobile is capable of an acceleration of about 1.7 m/s^2. At this rate, how long does it take to accelerate from 85 km/h to 100 km/h? >>

a = acceleration = (Vf - Vo)/T

where

a = 1.7 m/sec^2 (given)

Vf = final velocity = 100 km/hr (given)

Vo = initial velocity = 85 km/hr (given)

T = acceleration time

Substituting values,

1.7 = (100 - 85)*(1000/3600)/T

and solving for T,

T = (100 - 85)*(1000/3600)/1.7

T = (15*1000/3600)/1.7

T = 2.45 sec

Answer 2

1)  d = 16.5 m   t_total = 2.5 s    

v = d/t  .... d/v = t

t_total = 2.5 s  =  time_ball  +  time_sound

16.5/v_ball + 16.5/v_sound = 2.5 s

16.5/v_ball + 16.5/340 = 2.5

v_ball = 6.73 m/s

2)  dv/dt = a     (vf - vi)/ (tf - ti)

vf = 100km/h * ( 1 h/ 3600 s) * (1000 m / 1km) = 27.78 m/s

a = (27.78 m/s) / (6.6s)  =  4.208 m/s^2

a = 4.208 m/s^2

3)    Vf = Vo + at

   (Vf - Vo) = at

(100 km/h - 85 km/h)*(1000/3600) = a*t

4.1667 m/s = 1.7 m/s^2 * t

t = 2.45 s