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WITCHER [35]
3 years ago
10

A ball is thrown horizontally from a 90 m cliff and strikes the ground 70 m from the base, what is the initial velocity?

Physics
1 answer:
mash [69]3 years ago
7 0

Answer:

The initial velocity is 16 m/s

Explanation:

The position of the ball at a time t is given by the following vector:

r = (x0 + v0x · t, y0 + v0y · t + 1/2 · g · t²)

Where:

r = position vector at time t

x0 = initial horizontal position

v0x = initial horizontal velocity

t = time

y0 = initial vertical position

v0y = initial vertical velocity

g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive)

When the ball reaches the ground its position vector will be "r final" (see attached figure). The x-component of this vector is 70 m and the y-component is -90 m. Notice that the origin of the frame of reference is located at the throwing point (y0 and x0 = 0).  Then, we can use the equations for the x and y-component of "r" to obtain the time of flight and the initial velocity:

Using the equation for the y-component of the vector position:

y = y0 + v0y · t + 1/2 · g · t²        (y0 and v0y = 0)

-90 m = -1/2 · 9.8 m/s² · t²

-2 · -90 m/ 9.8 m/s² = t²

t = 4.3 s

Using the equation for the x-component of the vector position:

x = x0 + v0x · t

70 m = v0x · 4.3 s

v0x = 16 m/s

The initial velocity is 16 m/s

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Answer:

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Explanation:

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4 0
3 years ago
A watering can is most likely measured in which metric unit
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3 0
3 years ago
A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 43.0 vibrations
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Answer:

0.218

Explanation:

Given that

Total vibrations completed by the wave is 43 vibrations

Time taken to complete the vibrations is 33 seconds

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to solve this problem, we first find the frequency.

Frequency, F = 43 / 33 hz

Frequency, F = 1.3 hz

Also, we find the wave velocity. Which is gotten using the relation,

Wave velocity = 4.24 / 15

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2 years ago
If the range of a projectile's trajectory is six times larger than the height of the trajectory, then what was the angle of laun
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Answer:

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H = 1/8 g T^2   where T is total time in air  (2 t  = T)

R = V T cos θ       horizontal range

3/4 g T^2 = V T cos θ       6 H = R    given in problem

cos θ = 3 g T / (4 V)           (I)

Now t = V sin θ / g     time for projectile to fall from max height

T = 2 V sin θ / g

T / V = 2 sin θ / g

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