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3 years ago

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A horse canters away from its trainer in a straight line, moving 37 m away in 9.1 s. It then turns abruptly and gallops halfway

back in 1.8 s . Calculate its average speed for the entire trip.
Express your answer using two significant figures.
Calculate its average velocity for the entire trip, using "away from the trainer" as the positive direction.
Express your answer using two significant figures.

1 answer:

vesna_86 [32]3 years ago

3 0

Answer:

Average velocity = 1.69 m/s

Average speed = 5.09 m/s

Explanation:

Given that

Horse cover 37 m in 9.1 sec and 18.5 m in 1.8 sec.

As we know that

Average velocity = Displacement / Total time

Average speed = Total distance / Total time

Average velocity:

Average velocity = Displacement / Total time

Total displacement = 37 - 18.5 = 18.5 m

Total time = 9.1 + 1.8 =10.9 s

Average velocity = Displacement / Total time

Average velocity = 18.5 / 10.9

Average velocity = 1.69 m/s

Average speed:

Average speed = Total distance/ Total time

Total distance = 37 + 18.5 = 55.5 m

Total time = 9.1 + 1.8 =10.9 s

Average speed = Total distance/ Total time

Average speed = 55.5 / 10.9

Average speed = 5.09 m/s

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In a 49 s interval, 595 hailstones strike a glass window of an area of 0.954 m at an angle of 25° to the window surface. Each ha

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Average force on the window: 0.32 N

Explanation:

The average force exerted on the window is given by Newton's second law

$F=\frac{\Delta p}{\Delta t}$

where

$\Delta p$ is the net change in momentum of the hailstones in a time interval of $\Delta t$

In order to find the change in momentum, we have to consider only the component of the hailstone's momentum perpendicular to the window, therefore:

$p_i =m u sin \theta$ is the initial momentum of one hailstone, with

m = 7 g = 0.007 kg is the mass

$u=4.5 m/s$ is the initial speed

$\theta=25^{\circ}$ is the angle with the window

The final momentum is

$p_f = mv sin \theta$

where

v = 4.5 m/s is the final speed (the collision is elastic so the speed is equal, while the direction changes)

$\theta=-25^{\circ}$ (after the rebound, the direction has changed)

So the change in momentum of 1 hailstone is

$\Delta p = mv sin(-25^{\circ})-mu sin(25^{\circ})=-2mu sin(25^{\circ})=-0.0266 kg m/s$

We are interested only in the magnitude, so

$\Delta p = 0.0266 kg m/s$

There are 595 hailstones hitting the window in 49 s, so the total change in momentum is

$\Delta p = 595\cdot 0.0266 = 15.8 kg m/s$

And therefore, the average force on the window is

$F=\frac{\Delta p}{\Delta t}=\frac{15.8}{49}=0.32 N$

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3 years ago

A boy starts from point A and walks 3 meters toward the north, then turns around and walks 6 meters toward the south.

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Answer:

Total distance traveled = 9 m

Explanation:

Given:

Distance travel towards north = 3 meter

Distance travel towards south = 6 meter

Find:

Total distance traveled

Computation:

Total distance traveled = Sum of total distance

Total distance traveled = Distance travel towards north + Distance travel towards south

Total distance traveled = 3 m + 6 m

Total distance traveled = 9 m

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A firefighting crew uses a water cannon that shoots water at 25.0 m/s at a fixed angle of 53.0° above the horizontal. The fire-f

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Answer:

8.8 m and 52.5 m

Explanation:

The vertical component and horizontal component of water velocity leaving the hose are

$v_v = vsin(\alpha) = 25sin(53^0) = 25*0.8 = 19.97 m/s$

$v_h = vcos(\alpha) = 25cos(53^0) = 25*0.6 = 15 m/s$

Neglect air resistance, vertically speaking, gravitational acceleration g = -9.8m/s2 is the only thing that affects water motion. We can find the time t that it takes to reach the blaze 10m above ground level

$s = v_vt + gt^2/2$

$10 = 19.97t - 9.8t^2/2$

$4.9t^2 - 19.97t + 10 = 0$

$t= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$t= \frac{19.9658877511823\pm \sqrt{(-19.9658877511823)^2 - 4*(4.9)*(10)}}{2*(4.9)}$

$t= \frac{19.9658877511823\pm14.24}{9.8}$

t = 3.49 or t = 0.58

We have 2 solutions for t, one is 0.58 when it first reach the blaze during the 1st shoot up, the other is 3.49s when it falls down

t is also the times it takes to travel across horizontally. We can use this to compute the horizontal distance between the fire-fighters and the building

$s_1 = v_ht_1 = 15*0.58 = 8.8 m$

$s_2 = v_ht_2 = 15*3.49 = 52.5m$

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If the ball that is thrown downward has an acceleration of magnitude aaa at the instant of its release (i.e., when there is no l

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Explanation:

At the instant of release there is no force but an acceleration of a, this means the ball is falling freely under the force of gravity. Then the acceleration would be due to force of gravity and acceleration a = g =9.81 m/s^2.

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Answer:

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As it is mentioned there are no other factors affecting the growth rate, in 10years the planet will be filled to its carrying capacity.

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