PART a)
By energy conservation we can say
divide whole equation by mass "m" and plug in all given data
so gymnast will reach the floor with speed 5.21 m/s
PART b)
Now the gymnast bend her knees by 0.1 m and comes to rest
so here we will have
now the force on the gymnast will be
so during landing the force will be 6798.5 N
Answer:
a) 0 m/s
b) - 24 m/s
c) - 68 m
Explanation:
Given:
Initial distance = - 4 m
Initial velocity, u = 4 m/s
1) acceleration, a = - 2 m/s² for time, t = 2 seconds
thus,
velocity after 2 seconds will be
from Newton's equation of motion
v = u + at
v = 4 + (-2) × 2
v = 0 m/s
2) Velocity after 2 second is the initial velocity for this case
given acceleration = - 6 m/s² for 4 seconds
thus,
final velocity, v = 0 + ( - 6 ) × 4 = - 24 m/s
here the negative sign depicts the velocity in opposite direction to the initial direction of motion
thus, velocity after 6 seconds = - 24 m/s
3) Now,
Total displacement in 6 seconds
= Displacement in 2 seconds + Displacement in 4 seconds
From Newton's equation of motion
where,
s is the distance
u is the initial speed
a is the acceleration
t is the time
thus,
= +
= - 16 - 48
= - 64 m
Hence, the final displacement = - 64 - 4 = - 68 m