(1)
Cheetah speed:
Its position at time t is given by
(1)
Gazelle speed:
the gazelle starts S0=96.8 m ahead, therefore its position at time t is given by
(2)
The cheetah reaches the gazelle when . Therefore, equalizing (1) and (2) and solving for t, we find the time the cheetah needs to catch the gazelle:
(2) To solve the problem, we have to calculate the distance that the two animals can cover in t=7.5 s.
Cheetah:
Gazelle:
So, the gazelle should be ahead of the cheetah of at least
Let us consider two vectors A and B.
As per the question, the two vectors are perpendicular to each other.
Hence the angle between them
We are asked to calculate the resultant of these two vectors.
As per parallelogram law of vector addition, the resultant of two vectors are-
[cos90=0]
This is the way by which we can add two perpendicular vectors.
Answer
given,
Length of the string, L = 2 m
speed of the wave , v = 50 m/s
string is stretched between two string
For the waves the nodes must be between the strings
the wavelength is given by
where n is the number of antinodes; n = 1,2,3,...
the frequency expression is given by
now, wavelength calculation
n = 1
λ₁ = 4 m
n = 2
λ₂ = 2 m
n =3
λ₃ = 1.333 m
now, frequency calculation
n = 1
f₁ = 12.5 Hz
n = 2
f₂= 25 Hz
n = 3
f₃ = 37.5 Hz