Answer:
Kinetic energy of boy just before hitting the ground is [tex]\approx[/tex]1000 J.
Speed of boy just before hitting the ground is 7.67 m/s
or 17.16 mi/hr.
Explanation:
Given that:
Mass of boy = 75lb = 34 kg
Height, h = 10ft = 3m
To find:
Kinetic energy of boy when he hits the ground.
As per law of conservation of energy The potential energy gets converted to kinetic energy.
[tex]\therefore[/tex] Kinetic energy at the time boy hits the ground = Initial potential energy of the boy when he was at the Height 'h'
The formula for potential energy is given as:
[tex]PE = mgh[/tex]
Where m is the mass
g is the acceleration due to gravity, g = 9.8 [tex]m/s^2[/tex]
h is the height of object
Putting all the values:
PE = [tex]34 \times 9.8 \times 3 \approx 1000\ J[/tex]
Hence, Kinetic energy is [tex]\approx[/tex]1000 J.
Formula for Kinetic energy is:
[tex]KE = \dfrac{1}{2}mv^2[/tex]
where m is the mass and
v is the speed
Putting the values and finding v:
[tex]1000 = \dfrac{1}{2}\times 34 \times v^2\\\Rightarrow v^2 = 58.82\\\Rightarrow v = 7.67\ m/s[/tex]
Given that:
1 m = 1.094 yd and 1 mi = 1760 yd
[tex]\Rightarrow 1609\ m = 1\ mi[/tex]
Converting 7.67 m/s to miles/hour:
[tex]\dfrac{7.67 \times 3600}{1609}=17.16\ mi/h[/tex]