The work done to pull the sister back on the swing is equal to the increase in potential energy of the sister:

(1)
where m is the sister's mass, g is the gravitational acceleration and

is the increase in altitude of the sister with respect to its initial position.
By calling

the angle of the chain with respect to the vertical, the increase in altitude is given by

(2)
where L is the length of the chain.
Putting (2) inside (1), we find

from which we can find the mass of the sister:
1)
Answer:
Part 1)
H = 30.6 m
Part 2)
t = 2.5 s
Part 3)
t = 2.5 s
Part 4)

Explanation:
Part 1)
initial speed of the ball upwards

so maximum height of the ball is given by



Part 2)
As we know that final speed will be zero at maximum height
so we will have



Part 3)
Since the time of ascent of ball is same as time of decent of the ball
so here ball will same time to hit the ground back
so here it is given as
t = 2.5 s
Part 4)
since the acceleration due to earth will be same during its return path as well as the time of the motion is also same
so here its final speed will be same as that of initial speed
so we have

2)
Answer:
a = 9.76 m/s/s
Explanation:
As we know that the object is released from rest
so the displacement of the object in vertical direction is given as



3)
Answer:
v = 29.7 m/s
Explanation:
acceleration of the rocket is given as

time taken by the rocket
t = 0.33 min
final speed of the rocket is given as



4)
Answer:
Part 1)
y = 25.95 m
Part 2)
d = 6.72 m
Explanation:
Part 1)
As it took t = 2.3 s to hit the water surface
so here we will have



Part 2)
Distance traveled by it in horizontal direction is given as



Explanation:
Current output at the battery will be current of entire circuit, while the current through each bulb in the parallel circuit is the total current circuit.
So, current output through power supply is i and current through each component be
considering only three component.
Then in a parallel circuit
