If an arrow is shot straight upward on the moon with a velocity of 58 m/s, its height (in meters) after t seconds is given by s(t)=58t−0.83t2. what is the velocity of the arrow (in m/s) after 7 seconds? equation editorequation editor after how many seconds will the arrow hit the moon? with what velocity (in m/s) will the arrow hit the moon?

a)

b)

c)

Explanation:

From the exercise we know the arrow's equation of position

a) If we want to know the velocity of the arrow after t=7s we need to derivate the equation of position to get velocity

Now, we evaluate 7s in the equation

b) To find how much time does it take the arrow to hit the moon we need to evaluate s=0 at the equation of position in the vertical direction

Solving the quadratic equation using the following formula

or

Since time can not be zero the answer is t=70s

c) To calculate the arrow's velocity when it hits the moon we need to evaluate t=70s in the equation of velocity

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.