Answer:
Explanation:
We were told to calculate the speed of the ball,
Given speed of sound as 340 m
And we know that the sound of the ball hitting the pins is at 2.80 s after the ball is released from his hands.
Speed of ball = distance traveled/(time of hearing - time the sound travels).
Speed= S/t
Where S= distance traveled
t= time of hearing - time the sound travels
time=time for ball to roll+timefor sound to come back.
time of sound=16.5/340
=0.048529secs
solving for speedof ball
Then,Speed of ball = distance traveled/(time of hearing - time the sound travels).
=16.5/(2.80-0.048529) m/s = 5.997m/s
Therefore, the speed of the ball is
5.997m/s
Answer:at 21.6 min they were separated by 12 km
Explanation:
We can consider the next diagram
B2------15km/h------->Dock
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B1 at 20km/h
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V
So by the time B1 leaves, being B2 traveling at constant 15km/h and getting to the dock one hour later means it was at 15km from the dock, the other boat, B1 is at a distance at a given time, considering constant speed of 20km/h*t going south, where t is in hours, meanwhile from the dock the B2 is at a distance of (15km-15km/h*t), t=0, when it is 8pm.
Then we have a right triangle and the distance from boat B1 to boat B2, can be measured as the square root of (15-15*t)^2 +(20*t)^2. We are looking for a minimum, then we have to find the derivative with respect to t. This is 5*(25*t-9)/(sqrt(25*t^2-18*t+9)), this derivative is zero at t=9/25=0,36 h = 21.6 min, now to be sure it is a minimum we apply the second derivative criteria that states that if the second derivative at the given critical point is positive it means here we have a minimum, and by calculating the second derivative we find it is 720/(25 t^2 - 18 t + 9)^(3/2) that is positive at t=9/25, then we have our answer. And besides replacing the value of t we get the distance is 12 km.
Answer:A powder is an assembly of dry particles dispersed in air. If two different powders are mixed perfectly, theoretically, three types of powder.
Explanation:
Answer:
the period of the 16 m pendulum is twice the period of the 4 m pendulum
Explanation:
Recall that the period (T) of a pendulum of length (L) is defined as:
where "g" is the local acceleration of gravity.
SInce both pendulums are at the same place, "g" is the same for both, and when we compare the two periods, we get:
therefore the period of the 16 m pendulum is twice the period of the 4 m pendulum.
Explanation:
6a) Work = force × distance
W = Fd
W = (60 N) (10 m)
W = 600 J
6b) Change in energy = work
ΔKE = 600 J
7a) Kinetic energy is half the mass times the square of the velocity.
KE = ½ mv²
KE = ½ (0.4 kg) (25 m/s)²
KE = 125 J
7b) Work = change in energy. When the ball is stopped, it has zero kinetic energy.
W = ΔKE
W = 0 J − 125 J
W = -125 J
