Student is attempting to hit a target 4 meters from the edge of the desk that is 1.4 m tall marble rules of a table horizontally as shown below according to the above information in diagram what velocity must a marble have to strike the target?

The correct option is;

7.49 m/s

Explanation:

The time it takes the marble to fall vertically is given by the equation

s = u·t + 1/2·g·t²

Where;

s = The height of the table = 1.4 m

u = The initial vertical velocity = 0 (The marble is given only an initial horizontal push (velocity))

g = The acceleration due to gravity = 9.81 m/s²

t = The time it takes the marble to reach the ground 1.4 m below

Plugging in the values. gives;

1.4 = 0×t + 1/2 × 9.81 × t²

∴ t² = 1.4/(1/2 × 9.81) ≈ 0.28542 s²

t = √0.28542 ≈ 0.5342s

The horizontal range the marble is to cover in the approximately 1.87 seconds before it reaches the ground = 4 meters

Therefore, the velocity that allows the marble to reach 4 meters in 1.87 seconds is give as follows;

Velocity = Distance/Time = 4 m/(0.5342 s) ≈ 7.49 m/s

Therefore the horizontal velocity the marble must have to strike its target is approximately 7.49 m/s.

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