Question

An object is dropped from the top of a cliff 610 meters high. Its height above the ground t seconds after it is dropped is 610minus4.9t squared. Determine its speed 7 seconds after it is dropped.

Answer 1

Height after ts seconds is given by the expression

                         $H = 610-4.9t^2$

Taking derivative with respect to time

                         $\frac{dH}{dt} =0-9.8t$

This is the value of velocity after time t seconds, negative sign means velocity is towards downward direction.

v = 9.8t

After 7 seconds, v = 9.8*7 = 68.6 m/s

Speed after 7 seconds after it is dropped = 68.6 m/s