Answer:
4
Explanation:
The weight of the rock is W = mg = (80 kg) (10 m/s²) = 800 N.
The mechanical advantage is therefore 800 N / 200 N = 4.
Elastic potential energy stored in a spring is
(1/2) · (spring constant) · (stretch or compress)² .
PE = (1/2) · (100 N/m) · (0.1 m)²
PE = (50 N/m) · (0.01 m²)
PE = (50 · 0.01) (N · m / m²)
PE = 0.5 N · m
PE = 0.5 Joule
Weight = mass * gravity = 60 kg * 3.75 m/s² = 225 N
<span>Option D.</span>
Answer:
Part a)
![H = 44.1 m](https://tex.z-dn.net/?f=H%20%3D%2044.1%20m)
Part b)
![y = 13.48 m](https://tex.z-dn.net/?f=y%20%3D%2013.48%20m)
Part c)
![d = 8.86 m](https://tex.z-dn.net/?f=d%20%3D%208.86%20m)
Explanation:
Part a)
As we know that ball will reach at maximum height at
t = 3 s
now we will have
![t = \frac{v sin\theta}{g}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bv%20sin%5Ctheta%7D%7Bg%7D)
now we have
![3 = \frac{vsin\theta}{9.8}](https://tex.z-dn.net/?f=3%20%3D%20%5Cfrac%7Bvsin%5Ctheta%7D%7B9.8%7D)
![v sin\theta = 29.4 m/s](https://tex.z-dn.net/?f=v%20sin%5Ctheta%20%3D%2029.4%20m%2Fs)
Now maximum height above ground is given as
![H = \frac{v^2sin^2\theta}{2g}](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7Bv%5E2sin%5E2%5Ctheta%7D%7B2g%7D)
![H = \frac{29.4^2}{2(9.8)}](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7B29.4%5E2%7D%7B2%289.8%29%7D)
![H = 44.1 m](https://tex.z-dn.net/?f=H%20%3D%2044.1%20m)
Part b)
Height of the fence is given as
![y = (vsin\theta) t - \frac{1}{2}gt^2](https://tex.z-dn.net/?f=y%20%3D%20%28vsin%5Ctheta%29%20t%20-%20%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
![y = (29.4)(5.5) - \frac{1}{2}(9.8)(5.5^2)](https://tex.z-dn.net/?f=y%20%3D%20%2829.4%29%285.5%29%20-%20%5Cfrac%7B1%7D%7B2%7D%289.8%29%285.5%5E2%29)
![y = 13.48 m](https://tex.z-dn.net/?f=y%20%3D%2013.48%20m)
Part c)
As we know that its horizontal distance moved by the ball in 5.5 s is given as
![x = v_x t](https://tex.z-dn.net/?f=x%20%3D%20v_x%20t)
![97.5 = v_x (5.5)](https://tex.z-dn.net/?f=97.5%20%3D%20v_x%20%285.5%29)
![v_x = 17.72 m/s](https://tex.z-dn.net/?f=v_x%20%3D%2017.72%20m%2Fs)
now total time of flight is given as
![T = 3 + 3 = 6 s](https://tex.z-dn.net/?f=T%20%3D%203%20%2B%203%20%3D%206%20s)
so range is given as
![R = v_x T](https://tex.z-dn.net/?f=R%20%3D%20v_x%20T)
![R = (17.72)(6)](https://tex.z-dn.net/?f=R%20%3D%20%2817.72%29%286%29)
![R = 106.4 m](https://tex.z-dn.net/?f=R%20%3D%20106.4%20m)
so the distance from the fence is given as
![d = 106.4 - 97.5](https://tex.z-dn.net/?f=d%20%3D%20106.4%20-%2097.5)
![d = 8.86 m](https://tex.z-dn.net/?f=d%20%3D%208.86%20m)