Answer:
The angle is ![\theta = 15.48^o](https://tex.z-dn.net/?f=%5Ctheta%20%20%3D%20%2015.48%5Eo)
Explanation:
From the question we are told that
The distance of the dartboard from the dart is ![d = 3.66 \ m](https://tex.z-dn.net/?f=d%20%20%3D%20%203.66%20%20%5C%20m)
The time taken is ![t = 0.455 \ s](https://tex.z-dn.net/?f=t%20%3D%20%200.455%20%5C%20s)
The horizontal component of the speed of the dart is mathematically represented as
![u_x = ucos \theta](https://tex.z-dn.net/?f=u_x%20%3D%20%20ucos%20%5Ctheta)
where u is the the velocity at dart is lunched
so
![distance = velocity \ in \ the\ x-direction * time](https://tex.z-dn.net/?f=distance%20%3D%20%20velocity%20%5C%20in%20%5C%20the%5C%20%20x-direction%20%20%2A%20%20time)
substituting values
![3.66 = ucos \theta * (0.455)](https://tex.z-dn.net/?f=3.66%20%3D%20%20%20ucos%20%20%5Ctheta%20%2A%20%20%280.455%29)
=> ![ucos \theta = 8.04 \ m/s](https://tex.z-dn.net/?f=ucos%20%5Ctheta%20%3D%20%208.04%20%20%5C%20m%2Fs)
From projectile kinematics the time taken by the dart can be mathematically represented as
![t = \frac{2usin \theta }{g}](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B2usin%20%5Ctheta%20%7D%7Bg%7D)
=> ![usin \theta = \frac{g * t}{2 }](https://tex.z-dn.net/?f=usin%20%5Ctheta%20%3D%20%20%5Cfrac%7Bg%20%20%2A%20t%7D%7B2%20%7D)
![usin \theta = \frac{9.8 * 0.455}{2 }](https://tex.z-dn.net/?f=usin%20%5Ctheta%20%3D%20%20%5Cfrac%7B9.8%20%20%2A%200.455%7D%7B2%20%7D)
![usin \theta = 2.23](https://tex.z-dn.net/?f=usin%20%5Ctheta%20%3D%202.23)
=> ![tan \theta = \frac{usin\theta }{ucos \theta } = \frac{2.23}{8.04}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%20%5Cfrac%7Busin%5Ctheta%20%7D%7Bucos%20%5Ctheta%20%7D%20%20%3D%20%20%5Cfrac%7B2.23%7D%7B8.04%7D)
![\theta = tan^{-1} [0.277]](https://tex.z-dn.net/?f=%5Ctheta%20%20%3D%20%20tan%5E%7B-1%7D%20%5B0.277%5D)
![\theta = 15.48^o](https://tex.z-dn.net/?f=%5Ctheta%20%20%3D%20%2015.48%5Eo)
Force = (mass) x (acceleration) Newton's second law of motion.
Force = (2 kg) x (3 m/s²) = 6 newtons.
The distance is 30 km and the displacement is 22.4 km North East
Answer:
time will elapse before it return to its staring point is 23.6 ns
Explanation:
given data
speed u = 2.45 ×
m/s
uniform electric field E = 1.18 ×
N/C
to find out
How much time will elapse before it returns to its starting point
solution
we find acceleration first by electrostatic force that is
F = Eq
here
F = ma by newton law
so
ma = Eq
here m is mass , a is acceleration and E is uniform electric field and q is charge of electron
so
put here all value
9.11 ×
kg ×a = 1.18 ×
× 1.602 ×
a = 20.75 ×
m/s²
so acceleration is 20.75 ×
m/s²
and
time required by electron before come rest is
use equation of motion
v = u + at
here v is zero and u is speed given and t is time so put all value
2.45 ×
= 0 + 20.75 ×
(t)
t = 11.80 ×
s
so time will elapse before it return to its staring point is
time = 2t
time = 2 ×11.80 ×
time is 23.6 ×
s
time will elapse before it return to its staring point is 23.6 ns