Answer:
(a) 0.261 rad/s
(b) 1007.72 m
Explanation:
The angular velocity of the Ferris wheel is 150.0 revolutions per hour.
(a) To calculate the angular velocity of the wheel in units of radians per second, you take into account the following equivalence:
1 hour = 3600 seconds
1 revolution = 2π radians
You use the previous conversion factors:
In units of radians per seconds the wheel turns at 0.261 rad/s
(b) To find the arc length described by the wheel, you first calculate the angle described by the wheel in the time t, by using the following formula:
(1)
ω: angular velocity = 0.261 rad/s
t: time = 4.95 min
You first convert the time to units of seconds
Next, you replace the values of the parameters in the equation (1):
Next, you use the following formula for the arc length:
(2)
r: radius of the wheel = 13.0 m
You replace the values of the parameters in the equation (2):
The arc length described by the wheel is 1007.72m
Answer:
B, the car travels around a circular track at 30 m.
Explanation:
Given that,
Horizontal velocity of the object, v = 20 m/s
Height of the cliff, h = 125 m
We need to find the time that it takes the object to fall to the ground from the cliff is most nearly. It can be calculated using second equation of motion. Let us consider that the initial speed of the object is 0. So,
Here, a = g and u = 0
So, the object will take 5 seconds to fall to the ground from the cliff.
42) The sailboat travels east with velocity
, while the current moves south with speed
. Since the two velocities are perpendicular to each other, he resultant velocity will be given by the Pytagorean theorem:
and the direction is in between the two original directions, therefore south-east. So, the correct answer is
D) 42 mph southeast
43) Since the light moves by uniform motion, we can calculate the distance corresponding to one light year by using the basic relationship between velocity, space and time. In fact, we know the velocity:
and the time is one year, corresponding to:
therefore, the distance corresponding to one light year is:
Therefore, the correct answer is D.
44) For the purpose of the problem, we can assume that the light travels instantaneously from the flash to us (because the distances involved are very small), so the time between the flash and the thunder corresponds to the time it took for the sound to travel to us.
The speed of sound is
And since the time between the flash and the thunder is t=3 s, the distance is
Therefore, the correct answer is A) 3/5 mile.
