How to solve a motion equation word problem?

A cat jumps from a ledge that is meters off the ground to catch a hummingbird. While in the air, the center of mass of his motion is at a height given by the equation



h(t)=Ho+Vo*t-9.8*t^2













which holds right until he lands on the ground. He lands with a velocity of -7 meters per second, 1.2 seconds after starting the jump.



1) how high is the ledge?



2) what is the initial velocity?How to solve a motion equation word problem?2) h(t) = Ho + Vot - 9.8t^2

h'(t) = v(t) = Vo - 19.6t

-7 = Vo - 19.6(1.2)

-7 + 23.52 = Vo

16.52 = Vo



The initial velocity is 16.52 m/sec.



1) h(t) = Ho + 16.52t - 9.8t^2

0 = Ho - 15.52(1.2) - 9.8(1.2)^2

32.736 = Ho



The ledge is 32.736 m above the ground.



Since a = 9.8 m/sec^2, shouldn't the equation be h(t) = Ho + Vot - 4.9t^2?How to solve a motion equation word problem?Ho is the height of the ledge. So solve for Ho by plugging your know values into the given equation:



h(1.2) = 0 = Ho + Vo*1.2 - 9.8(1.2^2)



The height at t = 1.2 is zero because the cat lands on the ground.



If you've done derivatives, you solve the equation by taking the derivative of the height which gives you the vertical velocity as a function of time. If you haven't done derivatives, I would assume the initial velocity of the cat is zero. Hence Vo = 0. Or take the derivative:



h'(t) = V(t)



V(t) = Vo - 2*9.8t



Now you know that at t = 1.2 the velocity is -7 ms-1. So:



-7 + 2*9.8 = Vo



Now plug that back into the first equation and solve for the initial height.