Explanation:
Impulse momentum theorem is change in momentum is impulse.
Change in momentum = Impulse
Final momentum - Initial momentum = Impulse
Mass x Final velocity - Mass x Initial Velocity = Force x Time
Mass x Final velocity - Mass x Initial Velocity =Mass x Acceleration x Time
Final velocity - Initial Velocity = Acceleration x Time
Final velocity = 9.9 m/s
Initial Velocity = 3.7 m/s
Acceleration = 9.81 m/s²
Substituting
9.9 - 3.7 = 9.81 x Time
Time = 0.632 seconds
Time taken is 0.632 seconds
It will take the stone 0.6326secs to fall straight down to increase its speed from 3.7 m/s to 9.90 m/s
According to Newton's second law of motion;
F = ma
m is the mass of the object
a is the acceleration
The equation can also be expressed as:
[tex]F=m\frac{(v-u)}{t} \\Ft=m(v-u)\\mat=m(v-u)\\at=v-u\\t=\frac{v-u}{a}[/tex]
Given the follwing parameters;
v = 9.90m/s
u = 3.7m/s
a = 9.8m/s²
Substitute the given parameters into the formula to have:
[tex]t=\frac{9.9-3.7}{9.8}\\t= \frac{6.2}{9.8}\\t=0.6326secs[/tex]
Hence it will take the stone 0.6326secs to fall straight down to increase its speed from 3.7 m/s to 9.90 m/s
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