Question

Formula without time for final velocity of vertical component projectile motion

a) V_f = V_i + at
b) V_f = √(V_i^2 + 2ad)
c) V_f = V_i + d/t
d) V_f = 2d/t

Answer 1

The correct formula for the final velocity of a projectile's vertical motion without time is V_f = √(V_i^2 + 2ad), which uses initial velocity, acceleration due to gravity, and vertical displacement. (option b)

Step-by-step explanation:

The question pertains to the formula for the final velocity of vertical component of a projectile's motion, without the use of time. In this case, the correct formula would be option (b) Vf = √(Vi^2 + 2ad). This equation is derived from one of the kinematic equations for uniformly accelerated motion, which does not include the time variable.

To demonstrate how it is used, consider a projectile with an initial vertical velocity (Vi) and an acceleration due to gravity (a). If you know the vertical displacement (d), this formula allows you to find the final velocity just before impact.

Hence, the answer is option b

Answer 2

The correct formula for the final velocity of the vertical component in projectile motion is b)
`\(V_f = √(V_i^2 + 2ad)\)`.

Step-by-step explanation:

In projectile motion the vertical component of motion can be described by the kinematic equation for final velocity V_f initial velocity V_ iacceleration a and displacement d. The correct formula is given by
`\(V_f = √(V_i^2 + 2ad)\)` as represented by option b.

Firstly let's break down the formula: V_fis the final velocity V_i is the initial velocity a is the acceleration in this case due to gravity and d is the vertical displacement. The square root accounts for the combined effects of initial velocity and the product of acceleration and displacement.

To understand this conceptually consider that the final velocity is the result of the initial velocity plus the effects of acceleration and displacement. As an object moves vertically it experiences an acceleration due to gravity, and the displacement contributes to the overall change in velocity.

Mathematically the formula can be derived from the kinem tic equation
`(V_f^2 = V_i^2 + 2ad\)` by solving for V_f leading to
`\(V_f = √(V_i^2 + 2ad)\)`. This formula encapsulates the key factors influencing the final velocity in the vertical component of projectile motion.