Respuesta :
Explanation:
It is given that,
A golf ball is hit off a tee at the edge of a cliff. The x component is given by, x = 18 t
y component is given by, y = 4 t - 4.9 t²
Where x and y are in meters and t is in seconds.
(a) The ball’s position as a function of time, using the unit vectors is given by :
[tex]r=18t+(4t-4.9t^2)[/tex]
(b) Velocity, [tex]v=\dfrac{dr}{dt}[/tex]
[tex]v=\dfrac{d(18t+(4t-4.9t^2)}{dt}[/tex]
[tex]v=18+(4-9.8t)[/tex]
i.e. v = 18 i +(4 - 9.8t) j
(c) Acceleration vector, [tex]a=\dfrac{dv}{dt}[/tex]
[tex]a=\dfrac{d(18i+(4-9.8t)j}{dt}[/tex]
a = -9.8 j m/s²
(d) Expressions for the position at t = 3 s
[tex]r=18(3)i+(4(3)-4.9(3)^2)j[/tex]
r = (54 i - 32.1 j) m
Expressions for the velocity at t = 3 s
v = 18 i +(4 - 9.8(3)) j
v = (18 i -25.4 j) m/s
Expressions for the acceleration at t = 3 s
a = -9.8 m/s² j
Hence, this is the required solution.
A) The vector expression for the ball’s position as a function of time, using the given unit vectors is; R(t) = (18t)i + (4t - 4.9t²)j
B) The velocity expression for the ball as a function of time, using the given unit vectors is; V(t) = 18i + (4 - 9.8t)j
C) The acceleration expression for the ball as a function of time, using the given unit vectors is; a(t) = -9.8j
D) The position, velocity and acceleration of the ball at t = 3 s are;
R(3) = (54i - 32.1j) m
R(3) = (54i - 32.1j) mV(3) = (18i - 25.4j) m/s
R(3) = (54i - 32.1j) mV(3) = (18i - 25.4j) m/sa(3) = -9.8j m/s²
We are given the x and y coordinates distance in terms of t as;
x(t) = 18t
x(t) = 18ty(t) = 4t - 4.9t²
A) We want to write a vector for the balls' position as a function of time. This simply means the resultant of the unit vectors.
Thus;
R(t) = x(t)i + y(t)j
R(t) = (18t)i + (4t - 4.9t²)j
B) The velocity will be the derivative of the position with respect to time. Thus;
V(t) = R'(t)
V(t) = 18i + (4 - 9.8t)j
C) The acceleration vector as a unit of time will be the derivative of the velocity. Thus;
a(t) = V'(t)
a(t) = -9.8j
D) At t = 3 s
R(3) = (18 × 3)i + ((4 × 3) - (4.9 × 3²))j
R(3) = (54i - 32.1j) m
V(3) = 18i + (4 - (9.8 × 3))j
V(3) = (18i - 25.4j) m/s
a(3) = -9.8j
Read more at; https://brainly.com/question/10980150
