A woman stands at the edge of a cliff and throws a pebble horizontally over the edge with a speed of v0 = 20.5 m/s. The pebble leaves her hand at a height of h = 55.0 m
above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the pebble leaves the hand. Answer parts a-f.
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(a)The time taken for the pebble to reach the ground is approximately 2.01 seconds, and
(b) the horizontal distance traveled by the pebble is approximately 41.02 meters.
(c) The vertical distance traveled by the pebble is 55 meters.
(d) The initial vertical velocity of the pebble is 0 m/s because it is thrown horizontally.
(e) The vertical acceleration of the pebble is due to gravity and is approximately -9.8 m/s^2.
(f) The negative sign indicates that the pebble is moving downward.
a) To find the time taken for the pebble to reach the ground, we can use the equation for vertical motion:
h = (1/2)gt^2, where h is the vertical distance and g is the acceleration due to gravity.
Rearranging the equation, we have:
t = √((2h) / g), where t is the time taken.
Substituting the given values, we get:
t = √((2 * 55) / 9.8) ≈ 2.01 seconds.
b) The horizontal speed of the pebble remains constant throughout its motion. Therefore, the horizontal distance traveled by the pebble can be found by multiplying the horizontal speed by the time taken:
d = v0 * t, where d is the horizontal distance and v0 is the initial horizontal speed.
Substituting the given values, we have:
d = 20.5 * 2.01 ≈ 41.02 meters.
c) The vertical distance traveled by the pebble is given as 55 meters.
d) The initial vertical velocity of the pebble is 0 m/s because it is thrown horizontally.
e) The vertical acceleration of the pebble is due to gravity and is approximately -9.8 m/s^2.
f) The final vertical velocity of the pebble when it reaches the ground can be found using the equation:
v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
Since the initial vertical velocity is 0 m/s and the acceleration due to gravity is -9.8 m/s^2, we have:
v = 0 + (-9.8) * 2.01 ≈ -19.8 m/s.
The negative sign indicates that the pebble is moving downward.
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Related Questions
D 4.8
This is a harder question based on the Law of Conservation of Momentum. Take the time to work
your way through it. Start with a diagram.
A 400 kg bomb sitting at rest on a table explodes into three pieces. A 150 kg piece moves off to the
east with a velocity of 150 m s². A 100 kg piece moves off with a velocity of 200 m s at a direction of
south 60° west. What is the velocity of the third piece?
It is possible
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The velocity of the third piece is v₃ = -12500 kg·m/s / m₃
How do we calculate?The law of conservation of momentum states that the total momentum before the explosion is equal to the total momentum after the explosion.
velocity of the third piece = v₃.
The total initial momentum before the explosion = 0
The total final momentum after the explosion= 0
Initial momentum = 0 kg·m/s (since the bomb is at rest)
Final momentum = m₁v₁ + m₂v₂ + m₃v₃
m₁ = mass of the first piece = 150 kg
v₁ = velocity of the first piece = 150 m/s (to the east)
m₂ = mass of the second piece = 100 kg
v₂ = velocity of the second piece = 200 m/s (south 60° west)
m₃ = mass of the third piece = unknown
v₃ = velocity of the third piece = unknown
0 = (150 kg)(150 m/s) + (100 kg)(200 m/s)(cos(60°)) + (m₃)(v₃)
final momentum = 0 and hence v₃ is found as :
0 = 22500 kg·m/s - 10000 kg·m/s + (m₃)(v₃)
-12500 kg·m/s = (m₃)(v₃)
v₃ = -12500 kg·m/s / m₃
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Particles q₁ = -66.3 μC, q2 = +108 μC, and
q3 = -43.2 μC are in a line. Particles q₁ and q2 are
separated by 0.550 m and particles q2 and q3 are
separated by 0.550 m. What is the net force on
particle q₂?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
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F = (k * |q₁ * q₂|) / r²
Where:
F is the force between the particles,
k is the electrostatic constant (approximately 9 × 10^9 N m²/C²),
q₁ and q₂ are the magnitudes of the charges on the two particles, and
r is the separation between the particles.
Let's calculate the forces between q₁ and q₂ as well as q₂ and q₃ using the given values:
For q₁ and q₂:
F₁₂ = (9 × 10^9 N m²/C² * |-66.3 μC * 108 μC|) / (0.550 m)²
For q₂ and q₃:
F₂₃ = (9 × 10^9 N m²/C² * |108 μC * -43.2 μC|) / (0.550 m)²
To find the net force on q₂, we need to consider the direction of each force and add them up. Since q₁ and q₂ have opposite charges, the force F₁₂ will be negative (pointing left), and the force F₂₃ will be positive (pointing right).
Net force on q₂ = F₁₂ + F₂₃
Let's calculate the values:
Which statement best describes the refraction of light as it moves from air to glass?
A. Light bends due to the difference in the speed of light in air and glass.
B. Although the light bends, its speed remains the same as before.
C. Although the light changes speed, it continues in the same direction as before.
D. Light undergoes diffraction due to the difference in the speed of light in air and glass.
Answers
Explain the function of power supply, readout, peripheral, microcomputer, transducer and processor
Answers
The function of the power supply is to provide electrical energy to the device or system that needs it. The power supply converts the incoming voltage from the power source into a form that is usable by the device, such as DC voltage.
The readout is a device or component that displays data or information to the user. The readout could be a simple LED display or a complex graphical display.
A peripheral is a device or component that connects to a computer or other electronic device to provide additional functionality. Examples of peripherals include printers, scanners, and external hard drives.
A microcomputer is a type of computer that is designed to fit on a single microchip. Microcomputers are found in a wide range of devices, including smart phones, tablets, and embedded systems.
A transducer is a device that converts one form of energy to another. In electronics, transducers are commonly used to convert electrical energy into mechanical energy, or vice versa.
The processor is the central component of a computer or electronic device. The processor is responsible for executing instructions and controlling the other components of the system. The performance and capabilities of a device are largely determined by the speed and power of the processor.
The obliquity of the rotation of Uranus is over 90 degrees. Compared to the plane of the solar system, it rotates on its "side", unlike any other planet. It is surmised that this angle of rotation was caused by:
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7. Name the type of mirror used:-
(i) as a reflector in search light (iii) by the dentist
(ii) as side view mirror in vehicles. (iv) as a shaving mirror
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Answer:
1. Concave mirror
2. Convex mirror
3. Concave mirror
4. Concave mirror
Explanation:
Concave mirror is placed near on an object it displays a virtual image
One strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the first one. Assume both snowballs are thrown with a speed of 26.5 m/s. The first one is thrown at an angle of 58.0° with respect to the horizontal. Find a - At what angle should the second snowball be thrown to arrive at the same point as the first?, find b - How many seconds later should the second snowball be thrown after the first in order for both to arrive at the same time?
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The second snowball should be thrown at an angle of approximately 48.196° with respect to the horizontal to arrive at the same point as the first snowball.
the second snowball should be thrown 4.582 seconds later in order for both to arrive at the same time.
To find the angle at which the second snowball should be thrown, we can use the fact that the horizontal displacement of both snowballs must be the same.
Let's first find the horizontal and vertical components of the velocity for the first snowball. The initial speed is 26.5 m/s, and the angle is 58.0° with respect to the horizontal.
The horizontal component of the velocity for the first snowball is given by:
V1x = V1 * cos(angle1)
= 26.5 m/s * cos(58.0°)
= 26.5 m/s * 0.530
= 14.045 m/s
Now, let's find the vertical component of the velocity for the first snowball:
V1y = V1 * sin(angle1)
= 26.5 m/s * sin(58.0°)
= 26.5 m/s * 0.848
= 22.472 m/s
Since the vertical acceleration is the same for both snowballs (gravity), the time it takes for both to arrive at the same point is the same. Therefore, we can use the time of flight of the first snowball to calculate the vertical displacement for the second snowball.
The time of flight for the first snowball can be calculated using the vertical component of velocity and the acceleration due to gravity:
t = (2 * V1y) / g
= (2 * 22.472 m/s) / 9.8 m/s²
≈ 4.582 s
Now, let's find the vertical displacement for the second snowball:
Δy = V1y * t - (0.5 * g * t²)
= 22.472 m/s * 4.582 s - (0.5 * 9.8 m/s² * (4.582 s)²)
≈ 103.049 m
To find the angle at which the second snowball should be thrown, we can use the horizontal displacement and the vertical displacement:
tan(angle2) = Δy / Δx
= 103.049 m / (2 * 14.045 m/s * t)
= 103.049 m / (2 * 14.045 m/s * 4.582 s)
≈ 1.085
Now, we can find the angle2 by taking the arctan of both sides:
angle2 ≈ arctan(1.085)
angle2 ≈ 48.196°
Therefore,
To find how many seconds later the second snowball should be thrown, we can simply use the time of flight of the first snowball, which is approximately 4.582 seconds.
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A ball is thrown vertically upward with a speed of 15.0 m/s. Find a - How high does it rise? in meters, find b - How long does it take to reach its highest point? in seconds, find c - How long does the ball take to hit the ground after it reaches its highest point? in seconds, find d - What is its velocity when it returns to the level from which it started? in m/s.
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Given that the initial velocity at which the ball is thrown vertically upward is 15m/s. Let us also assume that the value of acceleration due to gravity (g) = 9.8m/s² and in this case, the value will be -9.8m/s² as the ball is moving against gravity.
a) To calculate how high the ball rises, we can use the kinematic equation:
v² = u² + 2gs......(i)
where v ⇒ final velocity
u ⇒ initial velocity
g ⇒ acceleration and,
s ⇒ displacement (the height)
The final velocity will be 0 when the ball reaches its maximum height.
Substituting the values in equation (i), we get
0² = 15² + (2*-9.8*s)
0 = 225 - 19.6s
Thus, s = 225/19.6 = 11.48 m.
Therefore, the ball rises approximately 11.48 meters.
b) To find the time taken to reach the highest point, we can use the kinematic equation,
v = u + gt......(ii)
where t = time
Substituting the values in equation (ii)
0 = 15 - 9.8*t
t = -15/ -9.8 = 1.53 seconds
Thus, the time taken to reach the highest point = 1.53 seconds.
c) To find the time taken for the ball to hit the ground after it reaches its highest point, we can use the equation,
s = ut +1/2gt².....(iii)
As the ball is moving downwards, the initial velocity, u will be 0m/s.
Thus, substituting the values in equation (iii), we get
11.48 = 0*t + 1/2*9.8*t²
11.48 = 4.9t²
t² = 2.34
Therefore t = 1.53 seconds
Thus, the time taken for the ball to hit the ground is 1.53 seconds.
d) To find the velocity at which the ball returns to the level from which it started, we can use the equation
v = u+ gt.....(iv)
v = 0 + 9.8*1.53
Thus, v = 14.99 ≅ 15 m/s
Therefore, the velocity when it returns to the level from which it started is 15m/s.
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