Question

A lunar lander is descending toward the moon's surface. Until the lander reaches the surface, its height above the surface of the moon is given by the equation y(t) = b - ct dt², where b = 750 m is the initial height of the lander above the surface, c = 63.0 m/s, and d = 1.04 m/s² is the initial velocity of the lander at t = 0?

Answer 1

The equation for the height of a lunar lander above the surface of the moon is y(t) = b - ct dt². To find the initial velocity of the lander, we differentiate the equation with respect to time and solve for d.

The equation for the height of a lunar lander above the surface of the moon is given by y(t) = b - ct dt². In this equation, b represents the initial height of the lander above the surface, c represents the rate at which the height changes with time, and d represents the initial velocity of the lander at t=0.

To find the initial velocity of the lander, we need to differentiate the equation with respect to time. The derivative of y(t) with respect to t is equal to -2ctd + d²t, which is equal to 0 at t=0. Solving this equation gives us d = 1.04 m/s².

Therefore, the initial velocity of the lander at t=0 is 1.04 m/s².