Question

An object is falling from a height of 7.5 meters. At what height will its velocity be 7 meters/second?

Answer 1

Answer:

5.0 m

Explanation:

The velocity of the object at time t is given by

$v=at$

where a=9.8 m/s^2 is the acceleration of gravity and t is the time. If we substitute v=7 m/s, we can find the time t at which the velocity became 7 m/s:

$t=\frac{v}{a}=\frac{7 m/s}{9.8 m/s^2}=0.71 s$

The height of the object at time t, h(t), is given by the equation

$h(t)=h_0 -\frac{1}{2}at^2$

where $h_0 = 7.5 m$ is the initial height. By substituting t=0.71 s inside the equation, we find the height h(t) at which the velocity is 7 m/s:

$h(0.71 s)=7.5 m- \frac{1}{2}(9.8 m/s^2)(0.71 s)^2=5.0 m$