Answer:
2 seconds
Explanation:
The function of height is given in form of time. For maximum height, we need to use the concept of maxima and minima of differentiation.

Differentiate with respect to t on both the sides, we get

For maxima and minima, put the value of dh / dt is equal to zero. we get
- 32 t + 64 = 0
t = 2 second
Thus, the arrow reaches at maximum height after 2 seconds.
Answer:
128 m
Explanation:
From the question given above, the following data were obtained:
Horizontal velocity (u) = 40 m/s
Height (h) = 50 m
Acceleration due to gravity (g) = 9.8 m/s²
Horizontal distance (s) =?
Next, we shall determine the time taken for the package to get to the ground.
This can be obtained as follow:
Height (h) = 50 m
Acceleration due to gravity (g) = 9.8 m/s²
Time (t) =?
h = ½gt²
50 = ½ × 9.8 × t²
50 = 4.9 × t²
Divide both side by 4.9
t² = 50 / 4.9
t² = 10.2
Take the square root of both side
t = √10.2
t = 3.2 s
Finally, we shall determine where the package lands by calculating the horizontal distance travelled by the package after being dropped from the plane. This can be obtained as follow:
Horizontal velocity (u) = 40 m/s
Time (t) = 3.2 s
Horizontal distance (s) =?
s = ut
s = 40 × 3.2
s = 128 m
Therefore, the package will land at 128 m relative to the plane
Answer:
The frequency of the oscillation is 0.9Hz
Explanation:
This problem bothers on simple harmonic motion of a spring
Given data
Mass of the child m= 25kg
Spring constant k=791 N/m
Amplitude a= 31cm
But the period of the motion as a result of the adults sholve is expressed as
T=2π√m/k
T=2*3.142√25/791
T=6.284√0.031
T=6.284*0.176
T=1.11 sec
But frequency F=1/T
F=1/1.11
F=0.9Hz
Explanation:
It is given that,
A particle starts from rest and has an acceleration function as :

(a) Since, 
v = velocity




(b) 
x = position



(c) Velocity function is given by :


t = 1 seconds
So, at t = 1 second the velocity of the particle is zero.
The best and most correct answer to the question is :
Alpha particles
Beta particles
Gamma rays
Cosmic radiation
Neutrons
Hope this helped you :)