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Svetlanka [38]
3 years ago
15

A 73 kg swimmer dives horizontally off a 462 kg raft initially at rest. If the diver's speed immediately after leaving the raft

is 5.54 m/s, what is the corresponding raft speed
Physics
1 answer:
murzikaleks [220]3 years ago
5 0

Answer:

Corresponding raft speed = -0.875 m/s (the minus sign indicates that the raft moves in the direction opposite to the diver)

Explanation:

Law of conservation of momentum gives that the momentum of the diver and the raft before the dive is equal to the momentum of the diver and the raft after the dive.

And since the raft and the diver are initially at rest, the momentum of the diver after the dive is equal and opposite to the momentum experienced by the raft after the dive.

(Final momentum of the diver) + (Final momentum of the raft) = 0

Final Momentum of the diver = (mass of the diver) × (diving velocity of the diver)

Mass of the diver = 73 kg

Diving velocity of the diver = 5.54 m/s

Momentum of the diver = 73 × 5.54 = 404.42 kgm/s

Momentum of the raft = (mass of the raft) × (velocity of the raft)

Mass of the raft = 462 kg

Velocity of the raft = v

Momentum of the raft = 462 × v = (462v) kgm/s

404.42 + 462v = 0

462v = -404.42

v = (-404.42/462) = -0.875 m/s (the minus sign indicates that the raft moves in the direction opposite to the diver)

Hope this Helps!!!

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A projectile is fired with an initial speed of 65.2 m/s at an angle of 34.5º above the horizontal on a long flat firing range. (
Margarita [4]

Answer:

A) h = 69.58 m

D) v = 58.12 \frac{m}{s}  (Speed magnitude)

α = 22.49° (Speed direction above the horizontal)

Explanation:

Conceptual analysis:

To solve this problem we consider the following concepts:

1) The projectile in its movement describes a curved line called a parabola, therefore two coordinates are required to fix the position at each instant of time, since the movement is performed in the X-Y plane.

The initial velocity (Vo) is tangent to the trajectory at the initial point and can be broken down into two components, one vertical (Voy) and one horizontal(Vox):

V_{ox} =  V_{o}Cos\alpha _{o} Formula (1)

V_{oy} =  V_{o}Sin\alpha _{o} Formula (2)

Where:

Vo: Initial velocity in m/s

\alpha_{o}: Initial angle above the horizontal in grades

2) The formula to calculate its velocity at any vertical position(y) is as follows:

v_{y}^{2} = v_{oy}^{2} -2gy Formula (3)

Where:

v_{f}^{2}: Final speed component in vertical direction in m/s

v_{oy}^{2}: Initial speed component in vertical direction in m/s

g: acceleration due to gravity in m/s2

3) The formulas to calculate the projectile velocity components at any time (t) are:

v_{x} = v_{ox} Because the movement is uniform in the x direction (constant speed)

v_{y} = v_{oy}-g*t Formula (4)  Because the movement is uniformly accelerated in the y direction

Known information:

We know the following data:

v_{o} = 65.2 \frac{m}{s}

\alpha _{o} = 34.5º above the horizontal

g=9.8 \frac{m}{s^{2}}

Development of the problem:

Initial speed components(Vox, Voy), (Formula (1), Formula (2)

v_{ox} =  65.2*Cos34.5 = 53.7\frac{m}{s}

v_{oy} =  65.2*Sin34.5 = 36.93\frac{m}{s}

A) Maximum height (h):

When the projectile reaches its maximum height (h) ,the speed component Vy = 0, then, we replace this value in the Formula (3):

0=(36.93)^2-2*9.8*h

h=\frac{ (36.93)^2}{2*9.8} = 69.58 m

D) Speed of the projectile 1.50s after firing

We replace t=1.5 s in the formula(4)

v_{y} = 36.93-9.8*1.5 = 22.23 \frac{m}{s}

v_{x} = v_{ox} = 53.7 \frac{m}{s}

v = \sqrt{53.7^{2}+22.23^{2}} = 58.12 \frac{m}{s}  (Speed magnitude)

\alpha = tan^{-1} (\frac{v_{y}}{v_{x}}) =  tan^{-1} (\frac{22.23}{53.7})

α = 22.49° (Speed direction above the horizontal)

6 0
3 years ago
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