Question

please

How fast should a girl weighing 180 N run so that her kinetic energy is 729 J ?

(g=10m/s^2)​

Answer 1

Provided that:

• Weight of a girl = 180 Newton
• Kinetic energy = 729 Joules
• g = 10 m/s sq.

To calculate:

• The girl's velocity

Solution:

• The girl's velocity = 9 m/s

Using concepts:

• Formula to calculate weight
• Formula of kinetic energy

Using formulas:

• Weight is given by,

• ${\small{\underline{\boxed{\sf{W \: = mg}}}}}$

• Kinetic energy is given by,

• ${\small{\underline{\boxed{\sf{E_k \: = \dfrac{1}{2} \: mv^2}}}}}$

Where, W denotes weight, m denotes mass, g denotes acceleration due to gravity, v denotes velocity and E_k denotes kinetic energy

Required solution:

~ Firstly let us calculate the mass of the girl by using the formula to calculate weight!

$:\implies \sf Weight \: = Mass \times Acceleration \: due \: to \: gravity \\ \\ :\implies \sf W \: = m \times g \\ \\ :\implies \sf W \: = mg \\ \\ :\implies \sf 180 \: = m(10) \\ \\ :\implies \sf \dfrac{180}{10} \: = m \\ \\ :\implies \sf 18 \: = m \\ \\ :\implies \sf m \: = 18 \: kg \\ \\ :\implies \sf Mass \: = 18 \: kg$

~ Now let us calculate the velocity of the girl by using the formula to calculate kinetic energy!

$:\implies \sf E_k \: = \dfrac{1}{2} \: mv^2 \\ \\ :\implies \sf 729 \: = \dfrac{1}{2} \times 18 \times v^2 \\ \\ :\implies \sf 729 \: = 1 \times 9 \times v^2 \\ \\ :\implies \sf 729 \: = 9 \times v^2 \\ \\ :\implies \sf \dfrac{729}{9} \: = v^2 \\ \\ :\implies \sf 81 \: = v^2 \\ \\ :\implies \sf \sqrt{81} \: = v \\ \\ :\implies \sf 9 \: = v \\ \\ :\implies \sf v \: = 9 \: ms^{-1} \\ \\ :\implies \sf Velocity \: = 9 \: ms^{-1}$