The speed is 0.956 m / s.
<u>Explanation</u>:
The kinetic energy is equal to the product of half of an object's mass, and the square of the velocity.
K.E = 1/2 
m 
where K.E represents the kinetic energy,
m represents the mass,
v represents the velocity.
K.E = 1/2 m
1.10 10^42 = 1/2 3.26 10^31
= (1.10 10^42 2) / (3.26 10^31)
v = 0.956 m / s.
Given :
Initial velocity, u = -6 m/s.
Time taken, t = 4 seconds.
Acceleration due to gravity, 
.( Here negative sign means downward direction )
To Find :
Velocity after 4 seconds.
Solution :
By equation of motion.
v = u + at
Here , a = g.
v = u + gt
v = -6 + (-9.8)×4
v = -6 + (-39.2)
v = -45.2 m/s
Therefore, velocity after 4 seconds is -45.2 m/s.
Hence, this is the required solution.
The second problem requires a figure to be answered. For the first problem
The acceleration of the sack is
1.5² - 0² = 2a(0.2)
a = 5.63 m/s2
The reaction of the ramp is
F = 8 kg (5.63 m/s2)
F = 45 N
Differentiate the kinematic equation involving time to get the rate of increase of the velocity.
Answer:
(a) 0.84 s
(b) 8.22 m/s
(c) 15.33 m/s
Explanation:
u = 0 , h = 3.45 m, g = 9.8 m/s^2
Let time taken to reach the water is t and the velocity at the time of hitting of water surface is v.
(a) Use first equation of motion
s = u t + 1/2 a t^2
3.45 = 0 + 0.5 x 9.8 x t^2
t = 0.84 second
(b) Use first equation of motion
v = u + a t
v = 0 + 9.8 x 0.84 = 8.22 m/s
(c) If h = 12 m
use third equation of motion
v^2 = u^2 + 2 g h
v^2 = 0 + 2 x 9.8 x 12
v = 15.33 m / s
9).
In a properly conducted experiment, the experimenter controls one part
of the experiment to see what the other parts do.
Example: Experiment to describe the effect of heat on ice.
Take two same-size ice cubes out of the same ice tray in the same fridge.
Place each one on a little temperature-controlled electric pad.
Turn one pad on, to make it warm. Leave the other pad turned off.
You CONTROL one part of the experiment: the amount of heat that
the ice cube gets.
You KNOW that the heat is the only thing different between the two
ice cubes. They're the same size. They were both made from
the same water, and froze in the same tray in the same fridge.
so
You KNOW that any difference will be the result of the heat on one of them.
You WATCH to see what happens to the one that gets the heat.
10).
An hypothesis is a prediction of what you believe may be true.
Once you have it, it's time to do an experiment to find out whether
your hypothesis is true.
Example:
I have an hypothesis. It predicts that when ice gets warm it melts.
Experiment:
Take two same-size ice cubes out of the same ice tray in the same fridge.
Set one ice cube down on the table.
Keep the other one in your hand.
The one in your hand melts while the one on the table is still solid.
Is the hypothesis correct ?
Maybe it is. Maybe it isn't.
We know that there's something about your hand that melts ice.
It may be the warmth. But it may be something else about human skin.
You'll need another experiment, slightly different, to find out if it's the warmth.
