Given:
Mass, m = 600000 g
Height, h1 = 38 m
Height, h2 = 14 m
Let's solve for the following:
• (a). Gravitational potential energy
To find the gravitational potential energy, apply the formula:
[tex]_GPE=m*g*h[/tex]Where:
m is the mass in kg = 600000 g = 600 kg
g is the acceleration due to gravity = 9.8 ms/s²
h2 is the height in meters over the second hill = 14 m
Input the values into the formula and solve for PE:
[tex]\begin{gathered} _GPE=600*9.8*14 \\ \\ =82320\text{ J} \end{gathered}[/tex]Therefore, the gravitational potential energy at the second hill is 82320 Joules
• (b),. Kinetic energy at the second hill
To find the kinetic energy, apply the formula:
[tex]KE=\frac{1}{2}mv^2=mg\Delta h=mg(h_1-h_2)[/tex]Where:
m is the mass
h1 = 38 m
h2 = 14 m
Thus, we have:
[tex]\begin{gathered} KE=600*9.8(38-14) \\ \\ KE=600*9.8(24) \\ \\ KE=141120\text{ J} \end{gathered}[/tex]• (c). Mechanical Energy.
To find the mechanical energy, apply the formula:
Mechanical Energy = Potential energy + Kinetic energy
Mechanical Energy = 82320 + 141120 = 223440 J
• (d). Speed of the car when it goes over the second hill which is 14 m.
To find the speed of the car, apply the formula:
[tex]KE=\frac{1}{2}mv^2[/tex]Where:
KE is the kinetic energy = 223440 J
m = 600 kg
v is the velocity.
Let's solve for v:
[tex]\begin{gathered} 223440=\frac{1}{2}*600*v^2 \\ \\ 223440=300v^2 \\ \\ v=\sqrt{\frac{223440}{300}} \\ \\ v=27.29\text{ m/s} \end{gathered}[/tex]The speed when it goes over the second hill is 27.29 m/s
ANSWER:
• (A). 82320 J
,• (b). 141120 J
,• (C). 223440 J
,• (d). 27.29 m/s
