Question

Astronauts on our moon must function with an acceleration due to gravity of 0.170g. A.) If an astronaut can throw a certain wrench 15.0m vertically upward on earth, how high could he throw it on our moon if he gives it the same starting speed in both places? The answer to this one is 88.2m B.)How much longer would it be in motion (going up and coming down) on the moon than on earth? I just need help on part b, if you please help me and show me all the steps.

Answer 1

Answer:

88.23525 m

17.07596 seconds

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity

On Earth

$v^2-u^2=2as\\\Rightarrow -u^2=2as-v^2\\\Rightarrow u=\sqrt{v^2-2as}\\\Rightarrow u=\sqrt{0^2-2\times -9.81\times 15}\\\Rightarrow u=17.15517\ m/s$

On Moon

$v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-17.15517^2}{2\times -9.81\times 0.17}\\\Rightarrow s=88.23525\ m$

The wrench could be thrown a distance of 88.23525 m on the Moon.

On Earth

$v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17.15517}{-9.81}\\\Rightarrow t=1.74874\ s$

The time the wrench is in the air on Earth is 1.74874+1.74874 = 3.49748 s

On Moon

$v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17.15517}{-9.81\times 0.17}\\\Rightarrow t=10.28672\ s$

The time the wrench is in the air on Earth is 10.28672+10.28672 = 20.57344 s

The difference in time is 20.57344-3.49748 = 17.07596 seconds

Answer 2

a)The distance at which the ball must  throw it on our moon if he gives it the same starting speed in both places will be 88.2325 m.

b)The time the wrench is in the air on the earth will be 20.57344.

What is velocity?

The change of displacement with respect to time is defined as the velocity. Velocity is a vector quantity. it is a time-based component.

The initial velocity of the throw from the Newtons second equation of the motion is found as;

$\rm v^2 = u^2 +2as \\\\ 0=u^2+2as \\\\ u=\sqrt{2gh} \\\\ u=-\sqrt{2 \times (-9.81)\times 15 }\\\\ u= 147.15517 \ m/sec$

The distance at which the ball must  throw it on our moon if he gives it the same starting speed in both places is found as;

$\rm v^2 -u^2=2as \\\\ s= \frac{v^2-u^2}{2a} \\\\ s=\frac{0^2-(17.15)^2}{2 \times (-9.81)\times 0.17 } \\\\ s=88.23525 \ m$

The distance at which the ball must  throw it on our moon if he gives it the same starting speed in both places will be 88.2325 m.

The time period on earth;

$\rm v=u+at \\\\ t = \frac{v-u}{a} \\\\ t= \frac{0-17.15517}{(-9.81} \\\\ t= 1.74874 \ sec$

The time the wrench is in air on earth is,

T=2t

T=2(1.7484 sec)

T=3.49 sec

The time period on the moon is;

$\rm v=u+at \\\\ t = \frac{v-u}{a} \\\\ t= \frac{0-17.15517}{(-.81)(0.17)} \\\\ t= 10.28672 sec$

The time the wrench is in the air on the earth is;

T=2t

T=2(10.28672)

T=20.57344

Hence,the time the wrench is in the air on the earth will be 20.57344.

To learn more about the velocity refer to the link ;

https://brainly.com/question/862972

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