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
Answer:
6.18 m/s
Explanation:
Roller skate collision
The final direction of the system (me=M + person=P) velocity vector is at an angle; Ф, to the direction running south to north. Apply the component form of the impulse-momentum equation, firstly;
x-axis component form (+x east);
+
+
=
+
Ф
60 ·8 + 0 = (60 + 80)
Ф
480 = 140
Ф................. (I)
y-axis component form (+y north);
+
+
=
+ 
Ф
0 + 80.9 = (60 + 80)
Ф
720=
140
Ф
140Vf=
Ф......................................(2)
Substituting (2) into (1) to give the angle;
480 = 720tan Ф
Ф = arctan(0.67) =33.69°.......................(3)
Evaluating (1) with (3) gives the velocity magnitude
480 = 140Vfsin 33.69°
Vf=6.18 m/s
note 1:
This angle corresponds to a direction; 90° - 33.69° = 56.31° north of east.
With gravitational acceleration at 9.8, initial height at 3.5m and distance at 22m the initial horizontal velocity is 26.03 ms and the flight time is .845 seconds
To solve this problem we will apply the concepts related to the Impulse which can be defined as the product between mass and the total change in velocity. That is to say

Here,
m = mass
Change in velocity
As we can see there are two types of velocity at the moment the object makes the impact,
the first would be the initial velocity perpendicular to the wall and the final velocity perpendicular to the wall.
That is to say,


El angulo dado es de 45° y la velocidad de 25, por tanto


The change of sign indicates a change in the direction of the object.
Therefore the impulse would be as


The negative sign indicates that the pulse is in the opposite direction of the initial velocity.
Answer: Neither Sandra nor Marissa will be in her THR zone.
Explanation:
1) Actual pulse of both Sandra and Marissa : 144 bpm
2) Decrease of 20 bpm ⇒ 144 bpm - 20 bpm = 124 bpm
3) Sandra's TRH is in the range 135 - 172 bpm.
Since 124 < 135, she will be below the range.
4) Marissa's TRH range is 143 - 176 bpm.
Since, 124 < 143, she is below the range
In conlusion, neither Sandra nor Marissa will be in her THR zone.