A cat is crouching on a ledge that is 10 feet above the ground, trying to ambush

Question

A cat is crouching on a ledge that is 10 feet above the ground, trying to ambush pigeons that fly by. a. Suppose that a pigeon flies by 4.5 feet above the cat, and that the cat jumps off the ledge with just enough vertical velocity, V to catch the pigeon. If the height of the cat is given by h(t)=?16t^2 + Vt + 10, And h'(t)= -32t + V. Find when the velocity is equal to zero in terms of V. This is the time at the maximum height. t max= ???? sec, Please help me, i am stuck and tried so many ways (how do i find tmax ??)

Explanation / Answer

h(t)=16t^2 + Vt + 10

velocity=v=h'(t)=-32t+V

v=0

t=V/32

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