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crimeas [40]
3 years ago
5

A long jumper leaves the ground at an angle of 25 degrees with respect to the horizontal with a resultant velocity of 30 ft/s. W

hat was the horizontal velocity of the jumper at takeoff? What was the vertical velocity at takeoff? How high did the COM rise above the point of takeoff?
Physics
1 answer:
astra-53 [7]3 years ago
5 0

Answer:

The horizontal component of the velocity is 27.19 ft/s

The vertical component of the velocity at takeoff is 12.68 ft/s

The vertical distance traveled by the jumper is 8.2 ft

Explanation:

Given;

angle of projection or takeoff, θ = 25°

the resultant velocity, v = 30 ft/s

The horizontal component of the velocity is given by;

v_x = vcos \theta\\\\v_x = 30 * cos(25)\\\\v_x = 27.19 \ ft/s

The vertical component of the velocity at takeoff is given by;

v_y = vsin \theta\\\\v_y = 30 * sin(25)\\\\v_y = 12.68 \ ft/s

The vertical distance traveled by the jumper is given by;

v_y_f^2 = v_y_o^2 +2(-g)h\\\\v_y_f^2 = v_y_o^2 -2gh\\\\0 = 12.68^2 - (2*9.8)h\\\\0 = 160.78 - 19.6h\\\\19.6h = 160.78\\\\h = \frac{160.78}{19.6}\\\\ h = 8.2 \ ft

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An archer shoots an arrow with a mass of 45.0 grams from bow pulled
Sladkaya [172]

Answer:

The force the archer need to pull in order to achieve the height is approximately 101.8 N

Explanation:

By energy conservation principle, puling an elastic bow with a force, for a given distance, performs work which is converted to the potential energy of the arrow at height

The given parameters are;

The mass of the arrow, m = 45.0 grams = 0.045 kg

The distance the elastic bow is pulled, d = 65.0 cm = 0.65 m

The height at which the arrow is reaches, h = 150.0 meters

Let 'F', represent the force the archer need to pull in order to achieve the height

Work done, W = Force × Distance moved in the direction of the force

Therefore;

The work done in pulling the arrow, W = F × d

By energy conservation, we have;

The work done in pulling the arrow, W = The potential energy gained by the arrow, P.E.

W = P.E.

The potential energy gained by the arrow, P.E. = m·g·h

Where;

m = The mass of the arrow

g = The acceleration due to gravity = 9.8 m/s²

h = The height the arrow reaches

∴ by plugging in the values, P.E. = 0.045 kg ×9.8 m/s² × 150 m = 66.15 J

W = F × d = F × 0.065 m

Also, W = P.E. = 66.15 J

∴ W = F × 0.065 m = 66.15 J

F × 0.065 m = 66.15 J

F = 66.15 J/(0.65 m) = 1323/13 N ≈ 101.8 N

The force the archer need to pull in order to achieve the height, F ≈ 101.8 N.

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2 years ago
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