If an arrow is shot upward on the moon with a velocity of 57 m/s its height (in meters) after t seconds is given by H= 57t-0.06t^2. With what velocity will the arrow hit the moon?

is it 57 m/s??

correct.

To find the velocity at which the arrow hits the moon, we can differentiate the height equation with respect to time (t).

Given: H = 57t - 0.06t^2

Differentiating H with respect to t:
dH/dt = 57 - 0.12t

The velocity is the derivative of height with respect to time, so we have:
Velocity = dH/dt = 57 - 0.12t

To find the velocity at which the arrow hits the moon, we need to determine the value of t when the arrow hits the moon.
When the arrow hits the moon, the height (H) will be zero.

Setting H to zero and solving for t:
0 = 57t - 0.06t^2

Rearranging the equation:
0.06t^2 - 57t = 0

Now, we can solve this quadratic equation to find the values of t.
Using factoring or quadratic formula, we find two possible solutions: t = 0 and t = 950.

Since we are interested in the velocity when the arrow hits the moon, we consider the positive value of t, which is t = 950 seconds.

Plugging this value into the velocity equation:
Velocity = 57 - 0.12(950)
Velocity = 57 - 114
Velocity = -57 m/s

Therefore, the arrow hits the moon with a velocity of -57 m/s. The negative sign indicates that the arrow is moving downward.