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Margarita [4]
4 years ago
13

Choose the letter for the acceleration of the ball during the upward motion after it is released. a) The acceleration is in the

negative direction and constant. b) The acceleration is in the negative direction and increasing. c) The acceleration is in the negative direction and decreasing. d) The acceleration is zero. e) The acceleration is in the positive direction and decreasing. ea) The acceleration is in the positive direction and increasing. ea) The acceleration is in the positive direction and constant
Physics
1 answer:
lianna [129]4 years ago
8 0

Answer:

Option (a)

Explanation:

If a body is thrown upwards, it's velocity goes on decreasing with constant rate. It is because an acceleration is acting on the body which is equal to acceleration due to gravity and acting downwards. The value of acceleration due to gravity is constant and always acting downwards.

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Answer:

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A boat crossing a 153.0 m wide river is directed so that it will cross the river as quickly as possible. The boat has a speed of
Lynna [10]

We have the relation

\vec v_{B \mid E} = \vec v_{B \mid R} + \vec v_{R \mid E}

where v_{A \mid B} denotes the velocity of a body A relative to another body B; here I use B for boat, E for Earth, and R for river.

We're given speeds

v_{B \mid R} = 5.10 \dfrac{\rm m}{\rm s}

v_{R \mid E} = 3.70 \dfrac{\rm m}{\rm s}

Let's assume the river flows South-to-North, so that

\vec v_{R \mid E} = v_{R \mid E} \, \vec\jmath

and let -90^\circ < \theta < 90^\circ be the angle made by the boat relative to East (i.e. -90° corresponds to due South, 0° to due East, and +90° to due North), so that

\vec v_{B \mid R} = v_{B \mid R} \left(\cos(\theta) \,\vec\imath + \sin(\theta) \, \vec\jmath\right)

Then the velocity of the boat relative to the Earth is

\vec v_{B\mid E} = v_{B \mid R} \cos(\theta) \, \vec\imath + \left(v_{B \mid R} \sin(\theta) + v_{R \mid E}\right) \,\vec\jmath

The crossing is 153.0 m wide, so that for some time t we have

153.0\,\mathrm m = v_{B\mid R} \cos(\theta) t \implies t = \dfrac{153.0\,\rm m}{\left(5.10\frac{\rm m}{\rm s}\right) \cos(\theta)} = 30.0 \sec(\theta) \, \mathrm s

which is minimized when \theta=0^\circ so the crossing takes the minimum 30.0 s when the boat is pointing due East.

It follows that

\vec v_{B \mid E} = v_{B \mid R} \,\vec\imath + \vec v_{R \mid E} \,\vec\jmath \\\\ \implies v_{B \mid E} = \sqrt{\left(5.10\dfrac{\rm m}{\rm s}\right)^2 + \left(3.70\dfrac{\rm m}{\rm s}\right)^2} \approx 6.30 \dfrac{\rm m}{\rm s}

The boat's position \vec x at time t is

\vec x = \vec v_{B\mid E} t

so that after 30.0 s, the boat's final position on the other side of the river is

\vec x(30.0\,\mathrm s) = (153\,\mathrm m) \,\vec\imath + (111\,\mathrm m)\,\vec\jmath

and the boat would have traveled a total distance of

\|\vec x(30.0\,\mathrm s)\| = \sqrt{(153\,\mathrm m)^2 + (111\,\mathrm m)^2} \approx \boxed{189\,\mathrm m}

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