Finding a Vector In Exercises 53-56, find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. ‖ u ‖ = 1 , θ u = 0 ∘ ‖ v ‖ = 3 , θ v = 45 ∘
Finding a Vector In Exercises 53-56, find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. ‖ u ‖ = 1 , θ u = 0 ∘ ‖ v ‖ = 3 , θ v = 45 ∘
Solution Summary: The author explains how the x -component and y — component of u+v are (3sqrt2+1).
Finding a Vector In Exercises 53-56, find the component form of
u
+
v
given the lengths of u and v and the angles that u and v make with the positive x-axis.
‖
u
‖
=
1
,
θ
u
=
0
∘
‖
v
‖
=
3
,
θ
v
=
45
∘
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
According to Newton's law of universal gravitation, the force F between two bodies of constant mass
GmM
m and M is given by the formula F =
, where G is the gravitational constant and d is the
d²
distance between the bodies.
a. Suppose that G, m, and M are constants. Find the rate of change of force F with respect to
distance d.
F' (d)
2GmM
b. Find the rate of change of force F with gravitational constant G = 6.67 × 10-¹¹ Nm²/kg², on
two bodies 5 meters apart, each with a mass of 250 kilograms. Answer in scientific notation,
rounding to 2 decimal places.
-6.67x10
N/m syntax incomplete.
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