Answer:
T = 1.2 s
T = 15.1 m = 15 m
Explanation:
This is a case of projectile motion:
TOTAL TIME OF FLIGHT:
The formula for total time of flight in projectile motion is:
T = 2 V₀ Sinθ/g
where,
T = Total Time of Flight = ?
V₀ = Launch Speed = 13.9 m/s
θ = Launch Angle = 25°
g = 9.8 m/s²
Therefore,
T = (2)(13.9 m/s)(Sin 25°)/(9.8 m/s²)
<u>T = 1.2 s</u>
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RANGE OF BALL:
The formula for range in projectile motion is:
R = V₀² Sin2θ/g
where,
R = Horizontal Distance Covered by ball = ?
Therefore,
T = (13.9 m/s)²(Sin 2*25°)/(9.8 m/s²)
<u>T = 15.1 m = 15 m</u>
Answer:
The wavelength of the visible line in the hydrogen spectrum is 434 nm.
Explanation:
It is given that, the wavelength of the visible line in the hydrogen spectrum that corresponds to n₂ = 5 in the Balmer equation.
For Balmer series, the wave number is given by :

R is the Rydberg's constant
For Balmer series, n₁ = 2. So,


or

So, the wavelength of the visible line in the hydrogen spectrum is 434 nm. Hence, this is the required solution.
Answer:
Diana's speed relative to ground is <u>16 km/h</u> in the direction of motion of train.
Explanation:
Given:
Velocity of train in forward direction is, 
Here, 
Velocity of Diana relative to train in the backward direction is, 
Negative sign implies backward motion or motion opposite to the direction of train's motion. Here, Diana is walking from front of train to back. So, Diana is moving in the opposite direction.
Now, we know that, for two bodies 'A' and 'B', velocity of 'A' relative to ground is given as:

Therefore, velocity of Diana relative to ground is given as:



So, Diana's speed relative to ground is 16 km/h in the direction of motion of train.
Answer:
The speed of the raft is 1.05 m/s
Explanation:
The equation for the position of the stone is as follows:
y = y0 + v0 · t + 1/2 · g · t²
Where:
y = height of the stone at time t
y0 = initial height
v0 = initial speed
t = time
g = acceleration due to gravity
The equation for the position of the raft is as follows:
x = x0 + v · t
Where:
x = position of the raft at time t
x0 = initial position
v = velocity
t = time
To find the speed of the raft, we have to know how much time the raft traveled until the stone reached the river. For that, we can calculate the time of free fall of the stone:
y = y0 + v0 · t + 1/2 · g · t² (v0=0 because the stone is dropped from rest)
If we place the origin of the frame of reference at the river below the bridge:
0 m = 95.6 m - 9.8 m/s² · t²
-95.6 m / -9,8 m/s² = t²
t = 3.12 s
We know that the raft traveled (4.84 m - 1.56 m) 3.28 m in that time, then the velocity of the raft will be:
x/t = v
3.28 m / 3.12 s = v
v = 1.05 m/s