Answer:
a)
, b) 
Explanation:
a) The Hooke's law states that spring force is directly proportional to change in length. That is to say:

In this case, the force is equal to the weight of the object:



The spring constant is:



b) The length of the spring is:




Answer:
The minimum speed when she leave the ground is 6.10 m/s.
Explanation:
Given that,
Horizontal velocity = 1.4 m/s
Height = 1.8 m
We need to calculate the minimum speed must she leave the ground
Using conservation of energy



Put the value into the formula




Hence, The minimum speed when she leave the ground is 6.10 m/s.
Answer:
The time it takes the proton to return to the horizontal plane is 7.83 X10⁻⁷ s
Explanation:
From Newton's second law, F = mg and also from coulomb's law F= Eq
Dividing both equations by mass;
F/m = Eq/m = mg/m, then
g = Eq/m --------equation 1
Again, in a projectile motion, the time of flight (T) is given as
T = (2usinθ/g) ---------equation 2
Substitute in the value of g into equation 2

Charge of proton = 1.6 X 10⁻¹⁹ C
Mass of proton = 1.67 X 10⁻²⁷ kg
E is given as 400 N/C, u = 3.0 × 10⁴ m/s and θ = 30°
Solving for T;

T = 7.83 X10⁻⁷ s