Answer:
magnitude = 7.446 km, direction = 75.22° north of east
Explanation:
From the questions,
To get the the magnitude of the resultant vector we use Pythagoras theorem
a² = b²+c²
From the diagram,
y² = 1.9²+7.2²
y² = 55.45
y = √(55.45)
y = 7.446 km.
The direction of the dolphin is given as,
θ = tan⁻¹(7.2/1.9)
θ = tan⁻¹(3.7895)
θ = 75.22° north of east
Hence the magnitude of the resultant vector = 7.446 km, and it direction is 75.22° north of east
Answer: deceleration of 
Explanation:
Given
Car is traveling at a speed of u=20 m/s
The diameter of the car is d=70 cm
It slows down to rest in 300 m
If the car rolls without slipping, then it must be experiencing pure rolling i.e. 
Using the equation of motion

Insert 

Write acceleration as 

So, the car must be experiencing the deceleration of
.
Explanation:
It is given that,
Mass of the crate, m = 50 kg
Force acting on the crate, F = 10 N
Angle with horizontal, 
Let N is the normal force acting on the crate. Using the free body diagram of the crate. It is clear that,


N = 486.57 N
or
N = 487 N
If a is the acceleration of the crate. The horizontal component of force is balanced by the applied forces as :




or

So, the normal force the crate and the magnitude of the acceleration of the crate is 487 N and
respectively.
Answer:
The temperature is 233.15 K
Explanation:
Recall the formula to convert degree Celsius (C) into Fahrenheit (F):

So if we want the value of degree C to be the same as the value of the degree F, we want the following: C = F
which replacing F with C on the right hand side of the equation above, allows us to solve for C:

This means that -40°C = -40°F
And this temperature in Kelvin is:
-40°C + 273.15 = 233.15 K
Answer:
h = 22.35 m
Explanation:
given,
initial speed of the rock,u = 0 m/s
length of the window,l = 2.7 m
time taken to cross the window,t = 0.129 s
Speed of the rock when it crosses the window


v = 20.93 m/s
height of the building above the window
using equation of motion
v² = u² + 2 g h
20.93² = 0² + 2 x 9.8 x h
h = 22.35 m
Hence, the height of the building above the top of window is equal to h = 22.35 m