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A sly 1.5-kg monkey and a jungle veterinarian with a blow-gun loaded with a tranquilizer dart are 25 m above the ground in trees 70 m apart. Just as the veterinarian shoots hori- zontally at the monkey, the monkey drops from the tree in a vain attempt to escape being hit. What must the minimum muzzle ve- locity of the dart be for the dart to hit the monkey before the mon- key reaches the ground?

Respuesta :

opudodennis

Answer:

31 m/s

Explanation:

Horizontal distance is given as 70 m and vertical distance is given as 25m hence time of flight is calculated by

[tex] t=\frac{d}{v_x}=\frac{70}{v_x}\)[/tex]  where d is the horizontal distance and V_{x} is the velocity we want

Taking the initial velocity as zero and acceleration due to gravity g=9.8 m/s^2

[tex]h=\frac{1}{2}gt^2\)[/tex] and to find time

[tex]t^{2}=2*25/9.8=2.26 seconds[/tex]

[tex](\frac{70}{v_x}=2.26\)[/tex]

[tex]\(v_x=31 m/s\)[/tex]

Therefore, minimal speed is 31 m/s

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