HW Physics Problem-I want to make sure I understand how to do this for an exam.

Question

An impala is an African antelope capable of a remarkable vertical leap. In one recorded leap, a 45 kg impala went into a deep crouch, pushed straight up for 0.21 s, and reached a height of 2.5 m above the ground.

-To achieve this vertical leap, with what force did the impala push down on the ground?

-What is the ratio of this force to the antelope's weight?

Answer 1

Lauren,

To reach a height h, the antelope's starting velocity v₀ must be such that

v²₀=2gh or v₀=Sqrt(2gh) (1)

To reach that velocity in time t, the antelope must get an average upward acceleration

a=(v₀/t) (2)

To get that acceleration, the antelope must push on the ground with such downward force F that the ground's (equal and opposite) reaction force be enough to 1. compensate the antilope's gravitation pull (it's weight weight at rest, W₀=mg) and on top of it, be able to give the antilope the needed acceleration a from (2)

Altogether,

F=mg+ma=m(g+a)=m(g+v₀/t)=m[ g+Sqrt(2gh)/t ] (3)

The rest is substituting the given data into(3)

Hope this was helpful

Best

Dr.Ariel B.