A tuning fork vibrates at a frequency of 512 hertz
2 answers:
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1)
The initial data of the projectile are:
is the initial height
is the initial speed of the projectile, so its components along the x- and y- directions are
The motion of the cannonball along the x-direction is a uniform motion with constant speed, while on the y-direction it is an uniformly accelerated motion with constant acceleration g=9.8 m/s^2 downward. So, the two equations of motion of the projectile along the two directions are:
2) 4.94 s
To determine how long the cannon ball was in the air, we need to find the time t at which the cannonball hits the ground, so the time t at which y(t)=0:
Solving the equation with the formula, we have:
which has two solutions:
t = -0.50 s
t = 4.94 s
Discarding the first solution which is a negative time so it has no physical meaning, the correct solution is
t = 4.94 s
3) 115.6 m
To determine how far the cannonball travelled, we need to find the value of the horizontal position x(t) when the ball hits the ground, at t=4.94 s. Substituting this value into the equation of motion along x, we find:
4) 2.22 s
The cannonball reaches its maximum height when the vertical velocity becaomes zero.
The vertical velocity at time t is given by
where
g = 9.8 m/s^2 is the acceleration due to gravity
Substutiting and solving for t, we find
5) 36.2 m
The maximum height reached by the cannon is equal to the vertical postion y(t) when the vertical velocity is zero, so when t=2.22 s. Substituting this value into the equation of the vertical motion, we find:
1) B) 500 J
The amount of work done is equal to the product between the force applied (F=100 N) and the distance covered by the box (d=5 m):
2) B) Tommy had a positive acceleration between noon and 12:30 pm.
In fact, Tommy's velocity increases between noon and 12.30 pm (at noon, he travels at 4 mph, while at 12.30 pm he travels at 6 pm). Since acceleration is equal to the rate of chang in velocity, an increase in velocity means a positive acceleration.
3) C) The gravitational forces of people is so small it is overshadowed by that of Earth
The magnitude of the gravitational force is given by:
where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects. From this formula we can understand that the gravitational force exerted by a man on another man is negligible compared to the gravitational force exerted by the Earth on a man, since the Earth's mass is much greater than the mass of a man.
4) C) Wrestler C
The force due to gravity is equal to the weight of the wrestler: , where m is the mass of the wrestler and g is the acceleration due to gravity. Since wrestler C has the greatest mass (171 pounds), it has the largest weight, so it experiences the largest force due to gravity.
5) the graph here is missing.
6) the graph here is missing.
7) C) Carrie is, because velocity includes speed plus direction, and both changed.
An object is accelerating when its velocity changes. But velocity includes both speed and direction: therefore, an object is accelerating when either its speed or its direction is changing. In this example, we are told that Carrie and Sam go up and down in the carousel, therefore their velocity is changing direction, so they are accelerating for sure.
8) C) Chemical energy changes to mechanical energy.
The energy of the battery is chemical energy, and this is converted into kinetic energy (due to the motion of the fan), which is mechanical energy.
9) A) Their displacement is the same, zero miles
Displacement is equal to the difference between the final position and the initial position. Since the mile consists of 4 entire laps, it means that the two guys will return at their starting point at the end of the mile: therefore, their displacement is zero.
10) A) Use an inclined plane of length 8 m.
If we want to use the same effort, we must keep the proportions of the inclined plane the same as in the first example. In the first example, the ratio between the length of the incline and its height is 4:1, and since in the second example the height is increased to 2 m, to keep the same proportions the new ratio should be 8:2, so the length of the inclined plane must be 2 m.