Answer:
Explanation:
ignoring air resistance, the kinetic energy at water impact will equal the potential energy converted
½mv² = mgh
v = √(2gh)
v = √(2(9.81)2.1) = 6.4188... m/s
after impact, an impulse will result in a change of momentum.
There is a downward impulse due to gravity equal to the weight of the stone and an upward average force due to water resistance and buoyancy force.
FΔt = mΔv
(F - mg)Δt = m(vf - vi)
(F - mg) = m(vf - vi)/Δt
F = m(vf - vi)/Δt + mg
F = m((vf - vi)/Δt + g)
F = 1.05(((½(-6.4188) - -6.4188)/ 1.83) + 9.81)
F = 12.14198...
F = 12.1 N
Answer:
(a) 41.75m/s
(b) 4.26s
Explanation:
Let:
Distance, D = 89m
Gravity,
= 9.8 m/
Initial Velocity,
= 0m/s
Final Velocity,
= ?
Time Taken,
= ?
With the distance formula, which is
D =
+ 
and by substituting what we already know, we have:
89 =
×9.8×
With the equation above, we can solve for
:

Now that we have solved
, we can use the following velocity formula to solve for
:
, where
is also equals to
, so we have

By substituting
,
, and
,
We have:

The work done to pull the sled up to the hill is given by

where
F is the intensity of the force
d is the distance where the force is applied.
In our problem, the work done is

and the distance through which the force is applied is

, so we can calculate the average force by re-arranging the previous equation and by using these data: