Answer:
750 J
Explanation:
lets convert mass into kg first , 150 /1000 = 0.15 kg
kinetic energy =
= ![\frac{0.15*100^{2} }{2} = 750 J](https://tex.z-dn.net/?f=%5Cfrac%7B0.15%2A100%5E%7B2%7D%20%7D%7B2%7D%20%20%3D%20750%20J)
Um student a because they were there a few seconds ahead
let the mass of Venus is M then mass of Saturn is 100 M
similarly if the radius of Venus is R then the radius of Saturn is 10 R
now the force of gravity on a man of mass "m" at the surface of Venus is given by
![F_1 = \frac{GMm}{R^2}](https://tex.z-dn.net/?f=F_1%20%3D%20%5Cfrac%7BGMm%7D%7BR%5E2%7D)
now similarly the gravitational force on the man if he is at the surface of Saturn
![F_2 = \frac{G*100M*m}{(10R)^2}](https://tex.z-dn.net/?f=F_2%20%3D%20%5Cfrac%7BG%2A100M%2Am%7D%7B%2810R%29%5E2%7D)
![F_2 = \frac{GMm}{R^2}](https://tex.z-dn.net/?f=F_2%20%3D%20%5Cfrac%7BGMm%7D%7BR%5E2%7D)
so here if we divide the two forces
![\frac{F_1}{F_2} = 1](https://tex.z-dn.net/?f=%5Cfrac%7BF_1%7D%7BF_2%7D%20%3D%201)
so here we can say
F1 = F2
so on both planets the gravitational force will be same
First, find the amount of time for the dart to hit the board using this equation: t = d/v
t = 2 m/ 15 m/s = 0.133 s
Then, find the height the dart has fallen from its initial point using this equation: h = 0.5gt²
h = 0.5(9.81 m/s²)(0.133 s)² = 0.0872 m or 8.72 cm
Since the diameter of the bull's eye is only 5 cm, and you started at the same level of the top of the bull's eye, that means the maximum allowance would only be 5 cm. Since it exceeded to 8.72 cm, it means that <em>Veronica will not hit the bull's eye.</em>