Question

Crickets can jump with a vertical velocity of up to 14 ft/s. Which equation models the height of such a jump, in feet, after t seconds? h(t) = –16t2 + v0t + h0

h(t) = –16t2 + v0t + 14

h(t) = –16t2 + 14t

h(t) = –16t2 + 14t + 14

Answer 1

acceleration is simplified by assuming it is the constant -g

a=-g we integrate this with respect to time to get v...

v=-gt+C where C is the initial velocity in this case 14ft/s so

v=-gt+14 integrate again to get the height function

h=(-gt^2)/2 +14t +C we are not given an initial height so C is 0

h(t)=14t-gt^2/2 letting g=32 and neatening up a bit...

h(t)=14t-16t^2