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Fudgin [204]
3 years ago
15

vector J is 3250m long in a 38.4 direction. Vector K is 1822 m long in a 58.8 direction. Find the magnitude and direction of the

ir vector sum
Physics
1 answer:
garik1379 [7]3 years ago
3 0

Answer:

The resultant vector has a magnitude of 4998 m and a direction of 45.7°.

Explanation:

The x component of the resultant vector is the sum of the x components of each individual vector.

x = 3250 cos 38.4 + 1822 cos 58.8

x = 3490.8

Similarly, the y component of the resultant vector is the sum of the y components of each individual vector.

y = 3250 sin 38.4 + 1822 sin 58.8

y = 3577.2

The magnitude can be found with Pythagorean theorem:

√(x² + y²)

√(3490.8² + 3577.2²)

4998

The direction can be found with trigonometry:

atan(y / x)

atan(3577.2 / 3490.8)

45.7°

The resultant vector has a magnitude of 4998 m and a direction of 45.7°.

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PE = kx^2/2
5 Nm = 50N/m (x^2)
x = 0.32 m

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3) A 900N mountain climber scales a 100m cliff. How much work is done by the mountain climber?
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[High Dive) above a pool of water. According to the announcer, the divers enter the water at a speed of 56 mi/h (25 m/s). (Air r
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Answer:

(a) The announcer's claim is incorrect because the divers enter at a speed of 20.4 and not 25 m/s as announced

(b)  it’s possible for a diver to enter the water with the velocity of 25 m/s if he has initial velocity of 14.4 m/s. The upward initial velocity can’t be physically attained

Explanation:

(a)

To find the final velocity V_{f} for an object traveling distance h taking the initial vertical component of velocity as V_{i} the kinematics equation is written as

V_{f}^{2}=V_{i}^{2}+2ah where a is acceleration

Substituting g for a where g is gravitational force value taken as 9.81

V_{f}^{2}=V_{i}^{2}+2gh

Since the initial velocity is zero, we can solve for final velocity by substituting figures, note that 70 ft is 21.3 m for h

V_{f}=\sqrt {(2gh)}= V_{f}=\sqrt {(2*9.81*21.3)}= 20.44275

Therefore, the divers enter with a speed of 20.4 m/s

The announcer's claim is incorrect because the divers enter at a speed of 20.4 and not 25 m/s as announced

(b)

The divers can enter water with a velocity of 25 m/s only if they have some initial velocity. Using the kinematic equation

V_{f}^{2}=V_{i}^{2}+2gh

Since we have final velocity of 25 m/s

V_{i}^{2}=2gh-V_{f}^{2}

V_{i}=\sqrt{(V_{f}^{2}-2gh)}

V_{i}=\sqrt{(25^{2}-2*9.81*21.3)}= 14.390761 m/s

Therefore, it’s possible for a diver to enter the water with the velocity of 25 m/5 if he has initial velocity of 14.4 m/s

In conclusion, the upward initial velocity can’t be physically attained

3 0
3 years ago
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