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You throw a ball horizontally with an initial speed of 15 m/s from a height of 1.5 meters. How long does it take the ball to land? a) 0.55 seconds b) 0.39 seconds c) 6.53 seconds d) 0.15 seconds In the previous question, How far in front of you does the ball land? a) 1.5 meters b) 9.7 meters c) 8.3 meters d) 6.6 meters

Answer :

Given data:

Initial speed;

[tex]u=15\text{ m/s}[/tex]

Height;

[tex]H=1.5\text{ m}[/tex]

The time of flight for horizontal projectile i s given as,

[tex]T=\sqrt[]{\frac{2H}{g}}[/tex]

Here, g is the acceleration due to gravity.

Substituting all known values,

[tex]\begin{gathered} T=\sqrt[]{\frac{2\times1.5\text{ m}}{9.8m/s^2}} \\ =0.55\text{ s} \end{gathered}[/tex]

Therefore, the ball will take 0.55 s to land. Hence, option (a) is the correct choice.

The horizontal range is given as,

[tex]R=u\sqrt[]{\frac{2H}{g}}[/tex]

Substituting all known values,

[tex]\begin{gathered} R=(15\text{ m/s})\times\sqrt[]{\frac{2\times1.5\text{ m}}{9.8\text{ m/s}^2}} \\ =8.29\text{ m} \\ \approx8.3\text{ m} \end{gathered}[/tex]

Therefore, the ball will cover a distance of 8.3 m. Hence, option (c) is the correct choice.

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