Answer:
a) t= 0.515 s
b) vf= 5.047 m/s
Explanation:
Because ball move with uniformly accelerated movement we apply the following formulas:
d= v₀t+ (1/2)*g*t² Formula (1)
vf= v₀+gt Formula (2)
Where:
d:displacement in meters (m)
t : time in seconds (s)
v₀: initial speed in m/s
vf: final speed in m/s
g: acceleration due to gravity in m/s²
Known data
v₀=0
d= 1.30 m
g= 9.8 m/s²
Problem development
a)
We appy the formula 1 to calculate the time (t):
d= v₀t+ (1/2)*g*t²
1.30= 0+ (1/2)* (9.8)*t²
1.30=4.9*t²
t²=1.30/4.9
t= 0.515 s
b) We appy the formula 2 to calculate the final speed (vf):
vf= v₀+gt
vf= 0+(9.8)*(0.515)
vf= 5.047 m/s
Answer:
hence the y - component of the velocity is 50m/s
Answer:
, inside the plane
Explanation:
We need to calculate the magnitude and direction of the magnetic field produced by each wire first, using the formula
where
is the vacuum permeability
I is the current
r is the distance from the wire
For the top wire,
I = 4.00 A
r = d/2 = 0.105 m (since we are evaluating the field half-way between the two wires)
so
And using the right-hand rule (thumb in the same direction as the current (to the right), other fingers wrapped around the thumb indicating the direction of the magnetic field lines), we find that the direction of the field lines at point P is inside the plane
For the bottom wire,
I = 5.90 A
r = 0.105 m
so
And using the right-hand rule (thumb in the same direction as the current (to the left), other fingers wrapped around the thumb indicating the direction of the magnetic field lines), we find that the direction of the field lines at point P is also inside the plane
So both field add together at point P, and the magnitude of the resultant field is:
And the direction is inside the plane.
Answer:
The Reynolds numbers for flow in the fire hose.
Explanation:
Given that,
Diameter = 6.40 cm
Rate of flow = 40.0 L/s
Pressure 
We need to calculate the Reynolds numbers for flow in the fire hose
Using formula of rate of flow
Where, Q = rate of flow
A = area of cross section
Put the value into the formula
We need to calculate the Reynolds number
Using formula of the Reynolds number
Where, 
=viscosity of fluid
=density of fluid
Put the value into the formula
Hence, The Reynolds numbers for flow in the fire hose.
Momentum = 0.5 * 4 = 2
to conclude the man’s velocity after he throws the piece of equipment, divide
this number by the man’s mass.
v = 2/90
This is about 0.0222 m/s. To know if he can move 6 meters at velocity in
4minutes, use the following equation.
d = v * t, t = 4 * 60 = 240 s
d = 2/90 * 240 = 5⅓ meters.
This is ⅔ of a meter from the spaceship. To know the velocity that he must have
to move 6 meter, use the same equation.
6 = v * 240
v = 6/240
This is about 0.00416 m/s.
His final momentum = 90 * 6/240 = 2.25
To know the velocity of the package, divide this number by the mass of the
package.
v = 2.25/0.5 = 4.5 m/s
