Explorers on a planet with a thin atmosphere want to measure the acceleration of gravity at its surface. So they use a spring gun to launch a ball bearing vertically upward from the surface with a launch velocity of 29 ms. If we denote by gs the acceleration of gravity in that planet, in ms2, then the ball bearing will move following the formula:

s(t) = 30(t) - [gs/2][t^2]

If the ball bearing reaches its maximum height 21 seconds after being launched, what is the value of gs?

The value of is .

Step-by-step explanation:

We know that the position function is given by

Velocity is defined as the rate of change of position. Therefore,

So, the velocity function is

When a body reaches a vertical velocity of zero, this is the maximum height of the body and then gravity will take over and accelerate the object downward. Thus,

We know that the ball bearing reaches its maximum height 21 seconds after being launched (t = 21 s).

So, the value of is .

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.