The relationships between the parameters of motion are given by the kinematic equations of motion without considering the cause of the motion
From the given information, the correct option from which the initial velocity can be found is the option A
A. [tex]\overset \rightarrow v = \overset \rightarrow v_0 + \overset \rightarrow a \cdot \Delta t[/tex]
Reason:
The given parameter of the motion of the skateboarder are;
Direction of motion of the skateboarder = Horizontal direction
Time after which the skateboarder lands on the ground = 3 seconds
Final velocity of the of the skateboarder = -4.5 m/s
Acceleration due to gravity, g = -9.8
Required:
The equation useful for finding the skateboarders initial velocity
Solution;
Initial vertical velocity = 0
Using the equation [tex]\overset \rightarrow v = \overset \rightarrow v_0 + \overset \rightarrow a \cdot \Delta t[/tex], where a = -g, we have;
Final vertical velocity of the skateboarder, [tex]v_y[/tex] = 0 - g·t
[tex]v_y[/tex] = 0 - 9.8 m/s² × 3 s = -29.4 m/s
[tex]v_y[/tex] = -29.4 m/s
The final vertical velocity of the skateboarder =-29.4 m/s
Therefore, from the first equation, the final vertical velocity can be determined, from which the initial horizontal component of the final velocity can be found, from [tex]v = \sqrt{v_x^2 + v_y^2}[/tex]
Therefore, given that the distance, Δx, is not given, the correct option from which the initial velocity can be found is [tex]\underline{\overset \rightarrow v = \overset \rightarrow v_0 + \overset \rightarrow a \cdot \Delta t}[/tex]
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