An 8-inch dinner knife is sitting on a circular plate so that its ends are on the edge of the plate. if the minor arc that is in
1 answer:
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Answer:
(a). The initial velocity is 28.58m/s
(b). The speed when touching the ground is 33.3m/s.
Explanation:
The equations governing the position of the projectile are
where is the initial velocity.
(a).
When the projectile hits the 50m mark, ; therefore,
solving for we get:
Thus, the projectile must hit the 50m mark in 1.75s, and this condition demands from equation (1) that
which gives
(b).
The horizontal velocity remains unchanged just before the projectile touches the ground because gravity acts only along the vertical direction; therefore,
the vertical component of the velocity is
which gives a speed of
If no frictional work is considered, then the energy of the system (the driver at all positions is conserved.
Let
position 1 = initial height of the diver (h₁), together with the initial velocity (v₁).
position 2 = final height of the diver (h₂) and the final velocity (v₂).
The initial PE = mgh₁ and the initial KE = (1/2)mv₁²
where g = acceleration due to gravity,
m = mass of the diver.
Similarly, the final PE and KE are respectively mgh₂ and (1/2)mv₂².
PE in position 1 is converted into KE due to the loss in height from position 1 to position 2.
Therefore
(KE + PE) ₁ = (KE + PE)₂
Evaluate the given answers.
A) The total mechanical energy of the system increases.
FALSE
B) Potential energy can be converted into kinetic energy but not vice versa.
TRUE
C) (KE + PE)beginning = (KE + PE) end.
TRUE
D) All of the above.
FALSE
Let
position 1 = initial height of the diver (h₁), together with the initial velocity (v₁).
position 2 = final height of the diver (h₂) and the final velocity (v₂).
The initial PE = mgh₁ and the initial KE = (1/2)mv₁²
where g = acceleration due to gravity,
m = mass of the diver.
Similarly, the final PE and KE are respectively mgh₂ and (1/2)mv₂².
PE in position 1 is converted into KE due to the loss in height from position 1 to position 2.
Therefore
(KE + PE) ₁ = (KE + PE)₂
Evaluate the given answers.
A) The total mechanical energy of the system increases.
FALSE
B) Potential energy can be converted into kinetic energy but not vice versa.
TRUE
C) (KE + PE)beginning = (KE + PE) end.
TRUE
D) All of the above.
FALSE
Answer:
7.9 m/s
Explanation:
When both balls collide, they have spent the same time for their motions.
Motion of steel ball
This is purely under gravity. It is vertical.
Initial velocity, <em>u </em>= 0 m/s
Distance, <em>s</em> = 4.0 m - 1.2 m = 2.8 m
Acceleration, <em>a</em> = g
Using the equation of motion
Motion of plastic ball
This has two components: a vertical and a horizontal.
The vertical motion is under gravity.
Considering the vertical motion,
Initial velocity, <em>u </em>= ?
Distance, <em>s</em> = 1.2 m
Acceleration, <em>a</em> = -<em>g </em> (It is going up)
Using the equation of motion
Substituting the value of <em>t</em> from the previous equation,
Taking <em>g</em> = 9.8 m/s²,
This is the vertical component of the initial velocity
Considering the horizontal motion which is not accelerated,
horizontal component of the initial velocity is horizontal distance ÷ time.
The initial velocity is