Answer:
vector quantities are resolved into their component form (along the x and y-axis) before adding them. Let us assume that two vectors are
→
a
=
x
1
^
i
+
y
1
^
j
and
→
b
=
x
2
^
i
+
y
2
^
j
, we can find the sum of two vectors as follows.
→
a
+
→
b
=
x
1
^
i
+
y
1
^
j
+
x
2
^
i
+
y
2
^
j
=
(
x
1
+
x
2
)
^
i
+
(
y
1
+
y
2
)
^
j
The direction of the sum of the vectors (with positive x-axis) is,
θ
=
tan
−
1
(
y
1
+
y
2
x
1
+
x
2
)
Answer:
a ) 540 ft /s
b ) .144° /s
Explanation:
Let at any moment h be the height of the rocket . The distance of rocket from camera will be R
R ² = 4000² + h²
Differentiating both sides with respect to t
R dR/dt = h dh/dt
dR/dt = h/R dh/dt
a ) Given speed of rocket
dh/dt = 900
h = 3000
R² = 4000² + 3000²
R = 5000
dR/dt = h/R dh/dt
= (3000 / 5000 ) X 900
dR/dt = 540 ft /s
b ) Let θ be angle of elevation at the moment .
4000 / R = cosθ
Differentiating with respect to t
- 4000 x 1 / R² dR/dt = - sinθ dθ / dt
4000 x ( 1/ 5000² ) x 540 = 3 /5 x dθ / dt
.0864 = 3/5 dθ / dt
dθ / dt = .144° /s
Answer:
vₓ = 5.5 mile / h and 
= 2.5 mile/h
Explanation:
This is a problem of adding vectors, but since the canoe and the river are in the same direction, we can make an ordinary sum, write the equations for each situation
I rowed down the river. In this case the speed of the canoe and the river are in the same direction, consequently, they add up
(vₓ + ) = d / 1.5
I rowed up. In this case the canoe and the river have reversed directions
(vₓ- ) = d / 4
Feel us two equations with two unknowns,
Let's start by adding the equations
2vₓ = d / 1.5 + d / 4
2vₓ = 12 (4 + 1.5) / 4 1.5
vₓ = 11/2
vₓ = 5.5 mile / h
Let's substitute in the first of the two equations to find the speed of the river
(vₓ +) = d / 1.5
= d / 1.5 - vr
= 12 / 1.5 -5.5
= 8-5.5
= 2.5 mile / h
Because temperature indicates the movement of heat, which means that thermal energy is temperature.
Explanation:
In short, when we switch off a branch, the remaining branch still forms a complete circuit with the battery, so electricity still pass through the remaining branch.
Technically speaking, the voltage in each branch is the same, and the resistance of the light bulb remains unchanged (neglect effect of temp.) by V=IR, the current should remain unchanged after switching off the other branch.
