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Understanding the Projectile Motion

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Calculations:
g = 9.81; (Acceleration due to gravity in m/s^2)
v = (Initial velocity)
theta = (Launch angle)
theta_rad = theta * %pi / 180 = (Convert angle from degrees to radians)
t_flight = 2 * v * sin(theta_rad) / g = (Calculate time of flight)
R = v * cos(theta_rad) * t_flight = (Calculate horizontal range)
t = linspace(0, t_flight, 100); (100 points for a smooth curve)
x = v * cos(theta_rad) * t; (Horizontal position as a function of time)
y = v * sin(theta_rad) * t - 0.5 * g * t.^2; (Vertical position as a function of time)
Table for Curve (x,y)
Q 01: What does the slope of a straight line represent?
  • (A) The y-intercept of the line
  • (B) The steepness or inclination of the line
  • (C) The perpendicular distance between the line and the origin
  • (D) The rate of change of the y-intercept

Q 02: Two lines are parallel if they have:
  • (A) Different slopes and different y-intercepts
  • (B) Different slopes and the same y-intercept
  • (C) The same slope and different y-intercepts
  • (D) The same slope and the same y-intercept

Q 03: What is the equation of a straight line in point-slope form?
  • (A) y = mx + c
  • (B) y = ax² + bx + c
  • (C) y - y₁ = m
  • (D) x = ay + b

Q 04: Perpendicular lines have slopes that are:
  • (A) Equal
  • (B) Negative reciprocals of each other
  • (C) Positive reciprocals of each other
  • (D) Zero

Q 05: The y-intercept of a straight line is represented by the value of:
  • (A) m
  • (B) c
  • (C) x
  • (D) y

Q 06: What does the distance formula |Ax₁ + By₁ + C| / √(A² + B²) measure?
  • (A) The slope of the line
  • (B) The y-intercept of the line
  • (C) The distance between two points on the line
  • (D) The perpendicular distance between a point and the line

Q 07: If two lines are perpendicular, what is the product of their slopes?
  • (A) 0
  • (B) 1
  • (C) -1
  • (D) Undefined

Q 08: What property do parallel lines possess?
  • (A) They intersect at a right angle
  • (B) They have the same slope and y-intercept
  • (C) They have the same slope and different y-intercepts
  • (D) They never intersect and remain equidistant

Q 09: In the equation y = mx + c, what does "m" represent?
  • (A) The y-intercept
  • (B) The perpendicular distance
  • (C) The slope
  • (D) The x-intercept

Q 10: What does linearity indicate in a straight-line relationship?
  • (A) The line is curvilinear
  • (B) The line is nonlinear
  • (C) The line is a linear relationship
  • (D) The line has no relationship between variables