if a car A moving with a velocity of 50 km/hr and car B moving with a velocity of 30 km/hr
a) find the relative velocity of object A with respect to object B when they are travelling in the same direction
b) find the relative velocity of object A with respect to object B when they are travelling in opposite direction
Answers
Answer:
sorry
Explanation:
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Answer:
follow the ecplanation
Explanation:
Motion of a Car Relative to a Truck
A truck is traveling south at a speed of 70 km/h toward an intersection. A car is traveling east toward the intersection at a speed of 80 km/h ((Figure)). What is the velocity of the car relative to the truck?
A truck is shown traveling south at a speed V sub T E of 70 km/h toward an intersection. A car is traveling east toward the intersection at a speed V sub C E of 80 km/h
Figure 4.27 A car travels east toward an intersection while a truck travels south toward the same intersection.
Strategy
First, we must establish the reference frame common to both vehicles, which is Earth. Then, we write the velocities of each with respect to the reference frame of Earth, which enables us to form a vector equation that links the car, the truck, and Earth to solve for the velocity of the car with respect to the truck.
Solution
The velocity of the car with respect to Earth is
→
v
CE
=
80
km
/
h
^
i
.
The velocity of the truck with respect to Earth is
→
v
TE
=
−
70
km
/
h
^
j
.
Using the velocity addition rule, the relative motion equation we are seeking is
→
v
CT
=
→
v
CE
+
→
v
ET
.
Here,
→
v
CT
is the velocity of the car with respect to the truck, and Earth is the connecting reference frame. Since we have the velocity of the truck with respect to Earth, the negative of this vector is the velocity of Earth with respect to the truck:
→
v
ET
=
−
→
v
TE
.
The vector diagram of this equation is shown in (Figure).
The right triangle formed by the vectors V sub C E to the right, V sub E T down, and V sub C T up and right is shown V sub C T is the hypotenuse and makes an angle of theta with V sub C E. The vector equation vector v sub C T equals vector C E plus vector E T is given. A compass is shown indicating north is up, east to the right, south down, and west to the left.
Figure 4.28 Vector diagram of the vector equation
→
v
CT
=
→
v
CE
+
→
v
ET
.
We can now solve for the velocity of the car with respect to the truck:
|
→
v
CT
|
=
√
(
80.0
km
/
h
)
2
+
(
70.0
km
/
h
)
2
=
106.
km
/
h
and
θ
=
tan
−
1
(
70.0
80.0
)
=
41.2
°
north of east.
Significance
Drawing a vector diagram showing the velocity vectors can help in understanding the relative velocity of the two objects.