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  • The Equation of Trajectory

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    The trajectory equation is the path taken by a particle during projectile motion. The following is the equation: y = x tanθ – gx2/2u2cos2θ Because this equation is similar to the parabola (y = ax + bx2), it is concluded that that projectile motion is always parabolic in character.

  • Horizontal Range 

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    It is defined as the horizontal distance covered to the maximum distance possible. The horizontal range is a distance (OB) is: OB = Horizontal component of velocity(ux) * Total time(t)    (ux = u cosθ and t = 2usinθ/g) That is, Range(R) = ucosθ * 2usinθ/g      Horizontal Range of the projectile is: Horizontal Range(R) =…

  • Maximum Height 

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    It is the particle’s highest point (point A). The vertical component of the velocity (Vy) will be zero when the ball reaches point A.  That is, 0 = (usinθ)2 – 2gHmax       ( S = Hmax, vy = 0 and uy = u sin θ ) The Maximum Height of the projectile is: Maximum Height (Hmax) =…

  • Time of Flight

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    It is the total amount of time the projectile remains in the air. In Y direction total displacement (Sy) = 0. Taking motion in Y direction, Sy = uyt – 1/2(gt2)    (Here, uy = u sinθ and Sy = 0) i.e.      0 = usinθ – 1/2(gt2) t = 2usinθ/g Time of Flight(t) = 2usinθ/g

  • Formulas and Concepts of Projectile Motion

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    The projectile motion is divided into two parts: a horizontal motion with no acceleration and a vertical motion with constant acceleration due to gravity. Consider the following example of a ball being launched at an angle from point O to the horizontal x-axis with an initial velocity of u: (Image will be uploaded soon) Differential…

  • Projectile Motion

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    The path that an object takes when thrown at an angle other than 90 degrees from a horizontal point is known as a trajectory, the object is known as a projectile, and the motion is defined as the projectile motion. Football, baseball, cricket ball, and any other object are instances of projectile motion. There are…

  • Example

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    A wave is y = 2sin(4t). Find out its amplitude. Solution: Given: wave equation y = 2sin (4t) using the amplitude formula, x = A sin(ωt + ϕ) When compared to the wave equation, A = 2 ω = 4 ϕ = 0 As a result, the wave’s amplitude is 2 units.

  • What is the Amplitude Formula?

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    The largest deviation of a variable from its mean value is referred to as amplitude. The sine and cosine functions can be calculated using the amplitude formula. A is the symbol for amplitude. The sine (or cosine) function can be written as follows: x = A sin (ωt + ϕ)   or   x =…

  • Equations for Wave Amplitude

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    Amplitude refers to the maximum change of a variable from its mean value (when the variable oscillates about this mean value). In to and fro motion of a particle about a mean position, it is the maximum displacement from its mean position. Similarly, amplitudes are defined for periodic pressure variations, periodic current or voltage variations,…

  • How Does the Spring Constant Depend on the Length?

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    Suppose we have a spring of 6 cm with a spring constant k. What happens if we split the spring into two bits of equal size? There will be a new spring constant for one of these shorter springs, which will be 2k. More generally, a spring’s spring constant is inversely proportional to the spring’s…