Consider the upward direction of motion as positive and downward direction of motion as negative.
a = acceleration due to gravity in downward direction = - 9.8 
v₀ = initial velocity of rock in upward direction = ?
v = final velocity of rock at the highest point = 0 
t = time to reach the maximum height = 4.2 sec
Using the kinematics equation
v = v₀ + a t
inserting the values
0 = v₀ + (- 9.8) (4.2)
v₀ = 41.2 
Answer:
L_max= 0
Explanation:
The formula for magnitude of maximum orbital angular momentum is given by

l= orbital quantum number
l= n-1
n= shell number or principal quantum number
for n=1 , l=0
therefore, 
L_max= 0
Answer:
x = 4.4719 m
Explanation:
For answer this we will use the law of the conservation of energy, where:

First, we will call:
: the car in rest
: when the spring is compressed
so:


where M is the mass of the car, g the gravity, h the altitude, K is the constant of the spring and X is the spring compressed in stopping the ore car. So, replacing values, we get:

solving for x:
x = 4.4719 m
Answer:
(a) 3.82 x 10⁷ m/s
(b) 4.5 MV/m
Explanation:
(a)
ΔV = change in the electric potential as the proton moves = 7.60 x 10⁶ Volts
q = magnitude of charge on proton = 1.6 x 10⁻¹⁹ C
v = speed gained by the proton
m = mass of proton = 1.67 x 10⁻²⁷ kg
Using conservation of energy
Kinetic energy gained by proton = Electric potential energy
(0.5) m v² = q ΔV
inserting the values
(0.5) (1.67 x 10⁻²⁷) v² = (1.6 x 10⁻¹⁹) (7.60 x 10⁶)
v = 3.82 x 10⁷ m/s
(b)
d = distance over which the potential change = 1.70 m
Electric field is given as
E = ΔV/d
E = 7.60 x 10⁶/1.70
E = 4.5 x 10⁶ V/m
E = 4.5 MV/m