Answer:
a)    x = v₀² sin 2θ / g
b)    t_total = 2 v₀ sin θ / g
c)    x = 16.7 m
Explanation:
This is a projectile launching exercise, let's use trigonometry to find the components of the initial velocity
         sin θ =  / vo
 / vo
         cos θ = v₀ₓ / vo
          v_{oy} = v_{o} sin θ
          v₀ₓ = v₀ cos θ
          v_{oy} = 13.5 sin 32 = 7.15 m / s
          v₀ₓ = 13.5 cos 32 = 11.45 m / s
a) In the x axis there is no acceleration so the velocity is constant
          v₀ₓ = x / t
           x = v₀ₓ t
the time the ball is in the air is twice the time to reach the maximum height, where the vertical speed is zero
           v_{y} = v_{oy} - gt
           0 = v₀ sin θ - gt
           t = v_{o} sin θ / g
          
we substitute
        x = v₀ cos θ (2 v_{o} sin θ / g)
        x = v₀² /g      2 cos θ sin θ
        x = v₀² sin 2θ / g
at the point where the receiver receives the ball is at the same height, so this coincides with the range of the projectile launch,
b) The acceleration to which the ball is subjected is equal in the rise and fall, therefore it takes the same time for both parties, let's find the rise time
at the highest point the vertical speed is zero
           v_{y} = v_{oy} - gt
           v_{y} = 0
            t = v_{oy} / g
            t = v₀ sin θ / g
as the time to get on and off is the same the total time or flight time is
            t_total = 2 t
            t_total = 2 v₀ sin θ / g
c) we calculate
           x = 13.5 2 sin (2 32) / 9.8
           x = 16.7 m
 
        
             
        
        
        
Answer:
No, there won't be a collision.
Explanation:
We will use the constant acceleration formulas to calculate,
v = u + a*t
0 = 25 + (-0.1)*t
t = 250 seconds (the time taken for the passenger train to stop)
v^2 = u^2 + 2*a*s
0 = (25)^2  + 2*(-0.1)*s
s = 3125 m (distance traveled by passenger train to stop)
If the distance traveled by freight train in 250 seconds is less than (3125-200=2925 m) than the collision will occur
Speed*time = distance
Distance = (15)*(250)
Distance = 3750 m
As the distance is way more, there won’t be a collision
 
        
             
        
        
        
Answer:
The fraction of the protons would have no electrons 
Explanation:
We are given that 
Amoeba has total number of protons=
Net charge, Q=0.300pC
Electrons are fewer than protons=
We have to find the fraction of protons would have no electrons.
The fraction of the protons would have no electrons
=
The fraction of the protons would have no electrons
=

Hence, the fraction of the protons would have no electrons 
 
        
             
        
        
        
Answer:

Explanation:
Given that,
Mass of a boy is 78 kg
Mass of a girl is 65 kg
We need to find the force of gravitational attraction between them if they are 2 m away.
The formula for the gravitational force is given by :

So, the force between them is  .
.